# Principle Component Analysis
library(readr)
library(ggplot2)
library(lattice)
library(ggridges)
library(ggvis)
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## resolution
library(ggthemes)
library(cowplot)
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## theme_map
library(gapminder)
library(gganimate)
## No renderer backend detected. gganimate will default to writing frames to separate files
## Consider installing:
## - the `gifski` package for gif output
## - the `av` package for video output
## and restarting the R session
##
## Attaching package: 'gganimate'
## The following object is masked from 'package:ggvis':
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## view_static
library(dplyr)
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## Attaching package: 'dplyr'
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## filter, lag
## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, union
library(tidyverse)
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## ✔ tidyr 1.3.0 ✔ forcats 1.0.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
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library(grid)
library(gridExtra)
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## combine
library(RColorBrewer)
library(readr)
#Covid-liver cancer Example
Cancer<- read_csv("~/Downloads/Cancer_Breast.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Survivor
## dbl (7): Age, Stage, Tumor Size, Regional Node Examined, Reginol Node Positi...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Cancer
## # A tibble: 379 × 8
## Survivor Age Stage `Tumor Size` Regional Node Exami…¹ Regin…² Survi…³ Sex
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Alive 68 1 4 24 1 60 0
## 2 Alive 50 2 35 14 5 62 0
## 3 Alive 58 3 63 14 7 75 0
## 4 Alive 58 1 18 2 1 84 0
## 5 Alive 47 2 41 3 1 50 0
## 6 Alive 51 1 20 18 2 89 0
## 7 Alive 51 1 8 11 1 54 0
## 8 Dead 40 2 30 9 1 14 0
## 9 Alive 40 4 103 20 18 70 0
## 10 Alive 69 4 32 21 12 92 0
## # … with 369 more rows, and abbreviated variable names
## # ¹​`Regional Node Examined`, ²​`Reginol Node Positive`, ³​`Survival Months`
str(Cancer)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Survivor : chr [1:379] "Alive" "Alive" "Alive" "Alive" ...
## $ Age : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
## $ Stage : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
## $ Tumor Size : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
## $ Regional Node Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
## $ Reginol Node Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
## $ Survival Months : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
## $ Sex : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "spec")=
## .. cols(
## .. Survivor = col_character(),
## .. Age = col_double(),
## .. Stage = col_double(),
## .. `Tumor Size` = col_double(),
## .. `Regional Node Examined` = col_double(),
## .. `Reginol Node Positive` = col_double(),
## .. `Survival Months` = col_double(),
## .. Sex = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
#Get the Correlations between the measurements
Cancer$Stage<-as.numeric(factor(Cancer$Stage, labels=c("1","2","3","4")))
Cancer1=cor(Cancer[-1])
colMeans(Cancer1)
## Age Stage Tumor Size
## 0.07928344 0.27473584 0.27737917
## Regional Node Examined Reginol Node Positive Survival Months
## 0.20965656 0.26124102 0.10305467
## Sex
## 0.13925661
library (ggplot2)
ggplot(Cancer, aes(x=Stage, fill=Survivor))+geom_boxplot()+ labs(title='Survivorship comparison')
ggplot(Cancer, aes(x=Survivor,y=Stage)) + geom_boxplot()
## From the plot we can see that the survival rate for stage 1-2 is more, while in stage 2-3 there are no survivors.
# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
Cancer_pca <- prcomp(Cancer[,-1],scale=TRUE)
Cancer_pca
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
##
## Rotation (n x k) = (7 x 7):
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional Node Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol Node Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6 PC7
## Age -0.41336263 -0.03629602 -0.00410619
## Stage -0.21766761 0.18269976 -0.69082826
## Tumor Size -0.13361696 0.13694401 0.71864375
## Regional Node Examined -0.03947383 0.57624593 0.00365182
## Reginol Node Positive 0.10540722 -0.76394463 -0.04789123
## Survival Months -0.63971799 -0.15748760 0.05900235
## Sex 0.58479969 0.07795267 -0.02241484
summary(Cancer_pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion 0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
## In Standard deviation we can infer that:
## PC1 is mostly driven by Tumor Size, Stage, and Reginol Node Positive, which all have relatively high loadings on this component.
## PC2 is mostly driven by Regional Node Examined, Reginol Node Positive, and Age, which all have relatively high loadings on this component.
## PC3 is mostly driven by Sex, Survival Months, and Tumor Size, which all have relatively high loadings on this component.
## There are negative loadings for some variables on certain PCs, indicating that they are negatively associated with those components. For example, Age has a negative loading on PC1, meaning that as PC1 increases, Age tends to decrease.
# sample scores stored in cancer_pca$x
# singular values (square roots of sevenvalues) stored in Cancer_pca$sdev
# loadings (eigenvectors) are stored in Cancer_pca$rotation
# variable means stored in Cancer_pca$center
# variable standard deviations stored in Cancer_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_Cancer <- Cancer_pca$sdev^2)
## [1] 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
names(eigen_Cancer) <- paste("PC",1:5,sep="")
eigen_Cancer
## PC1 PC2 PC3 PC4 PC5 <NA> <NA>
## 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
sumlambdas <- sum(eigen_Cancer)
sumlambdas
## [1] 7
propvar <- eigen_Cancer/sumlambdas
propvar
## PC1 PC2 PC3 PC4 PC5 <NA> <NA>
## 0.32068166 0.16823523 0.15164191 0.13436059 0.12587630 0.07245656 0.02674774
cumvar_Cancer <- cumsum(propvar)
cumvar_Cancer
## PC1 PC2 PC3 PC4 PC5 <NA> <NA>
## 0.3206817 0.4889169 0.6405588 0.7749194 0.9007957 0.9732523 1.0000000
matlambdas <- rbind(eigen_Cancer,propvar,cumvar_Cancer)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
## PC1 PC2 PC3 PC4 PC5 <NA> <NA>
## Eigenvalues 2.2448 1.1776 1.0615 0.9405 0.8811 0.5072 0.1872
## Prop. variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.0725 0.0267
## Cum. prop. variance 0.3207 0.4889 0.6406 0.7749 0.9008 0.9733 1.0000
summary(Cancer_pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion 0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
Cancer_pca$rotation
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional Node Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol Node Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6 PC7
## Age -0.41336263 -0.03629602 -0.00410619
## Stage -0.21766761 0.18269976 -0.69082826
## Tumor Size -0.13361696 0.13694401 0.71864375
## Regional Node Examined -0.03947383 0.57624593 0.00365182
## Reginol Node Positive 0.10540722 -0.76394463 -0.04789123
## Survival Months -0.63971799 -0.15748760 0.05900235
## Sex 0.58479969 0.07795267 -0.02241484
print(Cancer_pca)
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
##
## Rotation (n x k) = (7 x 7):
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional Node Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol Node Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6 PC7
## Age -0.41336263 -0.03629602 -0.00410619
## Stage -0.21766761 0.18269976 -0.69082826
## Tumor Size -0.13361696 0.13694401 0.71864375
## Regional Node Examined -0.03947383 0.57624593 0.00365182
## Reginol Node Positive 0.10540722 -0.76394463 -0.04789123
## Survival Months -0.63971799 -0.15748760 0.05900235
## Sex 0.58479969 0.07795267 -0.02241484
## Sample scores stored in Cancer_pca$x
Cancer_pca$x
## PC1 PC2 PC3 PC4 PC5
## [1,] -1.441559363 1.84595445 -0.3691842456 0.8313546497 -0.332307184
## [2,] 0.466697152 0.06803649 -0.6236808487 -0.3679040103 0.110810520
## [3,] 1.724644704 -0.46933933 -0.1593826887 0.5351088884 -1.007021612
## [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
## [5,] 0.084534880 -1.24252757 -1.5702796993 -0.3040439925 0.527096385
## [6,] -0.987174108 0.58301426 0.1669091720 -0.9999683133 -0.430923510
## [7,] -1.289312885 0.33343114 -1.1225709379 -0.4660831193 0.647838054
## [8,] 0.457476281 -0.43703336 -2.3348237400 -0.5798103154 1.901144959
## [9,] 5.013544810 -0.35127563 0.3138865965 -0.6789485742 -0.346406933
## [10,] 1.966110970 0.57900951 0.8436785098 1.1971488330 -2.024615276
## [11,] -1.709742154 0.39272616 -0.8797546127 1.0395229446 -0.421546565
## [12,] 1.323214712 -1.40692828 0.0010448762 -0.8532983622 -0.998148360
## [13,] -0.047344848 0.20982069 -0.8615166802 1.1288786920 -0.430771477
## [14,] -0.023379894 1.83512622 -0.8543600804 -0.5919635549 1.267459198
## [15,] 1.042993427 1.19479846 -0.1106365956 0.7578922926 -0.309831792
## [16,] -0.954171084 1.25373181 -0.8631921253 0.4922727293 0.235344753
## [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
## [18,] 0.248390384 0.43156365 -0.4623851738 -1.2333483190 0.363615703
## [19,] -0.386424810 -0.37494859 0.5477775527 -1.3442739171 -1.122742523
## [20,] -0.212235416 0.44848661 -0.0814638947 0.1978257208 -0.848560671
## [21,] 0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
## [22,] 0.547237523 0.35323566 -0.8945832960 0.4857434118 0.105717976
## [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
## [24,] 1.484574719 -1.12275223 0.4930197218 -0.8534326311 -1.510109489
## [25,] 0.730385134 3.01009366 1.5328340955 -0.0845516282 -0.807050880
## [26,] 1.384044724 2.86730858 0.7935319092 0.4879719811 -0.466990302
## [27,] 2.503197607 1.86942247 1.6035708576 -1.0898911376 -0.702827024
## [28,] -1.094732396 0.13919430 -0.2430526831 -1.3348711724 0.009704223
## [29,] -0.040233637 0.24894946 -0.5823916977 0.1870202613 -0.228150297
## [30,] -0.913495245 -0.27255918 -0.2249052502 0.7136559763 -1.283048492
## [31,] 0.044817272 -1.24749459 -1.5147400984 -0.3403352312 0.475434709
## [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835 0.691915088
## [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
## [34,] -0.860691537 1.17774354 -0.4731321013 0.2383866081 -0.049714847
## [35,] 1.293140200 1.12837700 -1.0955034983 -0.3513923420 1.283108823
## [36,] -1.575412171 -0.65517742 1.1178980897 -0.0145585733 1.416899251
## [37,] 0.505620687 0.48204717 0.6768751198 0.9826148200 2.080438807
## [38,] -1.445729993 -0.53420180 2.0397881463 -0.4191403509 0.606045480
## [39,] -0.240634131 -1.38008841 1.2981310791 0.0234566336 0.948153836
## [40,] -0.335231355 -0.71567154 2.2622815166 -0.2598837684 0.304358552
## [41,] 2.392046521 -0.75381886 0.6808155988 1.7849935943 1.462378918
## [42,] -1.496209472 -0.05147919 0.8362058172 1.4463882147 1.234755769
## [43,] -1.238156754 -1.73396163 1.0838915624 1.1966166369 0.342914980
## [44,] -0.122858339 -0.41520397 1.7259286489 0.2467343049 0.834734733
## [45,] -1.614959830 -0.21262796 0.8270352673 0.5084458503 1.653782254
## [46,] 0.653344872 -1.45282335 1.6923961454 1.7730389364 -0.346353752
## [47,] -0.903132282 0.00288121 0.2891894480 -0.3828977838 2.883679498
## [48,] -1.570956435 -0.13307164 0.7378711359 1.2691205943 1.372131721
## [49,] 0.407142180 -0.18484286 1.8224576827 0.3406571927 0.900265041
## [50,] -2.095133885 -0.24603762 1.3075254314 1.5865972660 0.515650798
## [51,] 0.145196356 -0.72051716 1.2885099274 -1.1072761596 1.854988517
## [52,] 0.438754344 -1.67207421 0.9831353778 2.3512915236 -0.039137939
## [53,] 2.005777230 -2.95342227 1.2688959631 1.7356814675 -0.406467811
## [54,] 1.526981600 -1.02119752 1.4223445513 1.8001650835 0.106389455
## [55,] -1.762004433 0.13389155 1.3060891880 0.4365138287 1.220327765
## [56,] -1.584099552 -0.27233552 1.1461680461 0.3643457178 1.304773967
## [57,] -0.496130040 0.33490544 0.2711418287 0.1648088615 -1.311783436
## [58,] -0.310631363 3.07311289 1.8743230894 -1.7983452746 -1.034356670
## [59,] -1.133478035 0.41599332 -0.4379284603 -0.8528069490 0.092369673
## [60,] -1.203472671 0.78226143 -0.1914939617 -0.4844823758 -0.219974275
## [61,] -0.899762531 1.31926126 0.1811318594 -0.4938217806 -0.418037102
## [62,] -1.006446958 0.35539993 -1.2221294160 -0.3469217710 0.736595283
## [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576 0.044579623
## [64,] 1.712300783 -0.45593265 -0.1013381728 0.5911078860 -1.251280484
## [65,] -1.263885916 1.17224839 -0.6291534095 0.9206949813 -0.255173442
## [66,] -1.604219653 -0.82712464 0.0494208809 -1.5797529143 -0.620332594
## [67,] 4.488026052 1.14176192 -0.1231038156 -1.5112898673 1.345935978
## [68,] -0.665172931 0.68451038 0.1453995807 -2.0258292592 0.217431325
## [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
## [70,] -1.130422629 0.23695569 -0.1769384999 -0.7612337767 -0.266397542
## [71,] 3.316812797 -1.81535426 0.5502180418 -0.2694003925 -1.764262412
## [72,] 2.172380940 2.85911092 -0.9844345887 1.6403461146 1.175874251
## [73,] 0.572326326 -0.34757898 -1.0234096521 -2.0869344002 1.187096201
## [74,] -1.827615023 0.62057292 0.3016558087 0.2426806849 -1.315635893
## [75,] 0.720276568 1.70219107 0.6872975038 0.8005007414 -1.037240682
## [76,] 0.849193077 -1.14260361 0.1217975270 -0.0272015985 -1.564340163
## [77,] -0.640547040 -0.61272303 1.3854969929 1.5959470836 0.358667424
## [78,] -0.095120639 -2.25942107 1.7743414136 -0.8570595769 0.490508151
## [79,] -0.045215749 -1.67214619 1.1930256589 0.3311124134 0.788844783
## [80,] -1.769164273 -0.22777378 0.5215512977 1.9330657865 1.230687259
## [81,] 0.718379560 0.42702578 2.7049430509 0.0009902972 0.427134177
## [82,] -1.678008963 -0.30727716 0.8345249461 1.7090923528 0.957971947
## [83,] -0.895860760 -0.84819969 1.0351097886 1.6955225348 0.543187444
## [84,] -1.627068924 -1.17405222 0.1883777552 0.6241466387 1.941501550
## [85,] -1.331489281 -0.34160016 0.9121167916 0.1344506975 1.691751149
## [86,] 0.909892498 -0.53731582 1.4060161653 -0.0311065615 1.547734256
## [87,] 2.680823986 -2.87516871 1.2736995009 0.6959415006 0.332021211
## [88,] 1.353531002 -2.37316783 1.3254482077 0.7127875562 0.214693076
## [89,] -1.678967186 -0.70552936 1.6695940259 0.1038284595 0.653638646
## [90,] -2.304099591 -0.48981820 1.6210427235 0.9780934643 0.289061393
## [91,] 0.741204117 -2.34543537 1.4452706433 0.5998522096 0.088681106
## [92,] -0.809147683 -0.48805441 0.7203787577 -1.4686194537 2.727281577
## [93,] -0.790428226 -1.28394744 1.3498973595 1.2856985141 0.289629154
## [94,] 1.549314451 1.05942412 1.1109895492 0.1457696503 2.619577831
## [95,] -1.647991336 -0.27927996 1.6891990873 0.5048525410 0.651509510
## [96,] -0.268121798 -0.13194343 0.7385162603 1.3684964706 1.386087535
## [97,] -0.103534223 -1.33945241 -0.5191543874 1.0167737783 2.587808079
## [98,] -0.776307350 -0.99454099 1.0504553950 1.2109563269 0.697921783
## [99,] 1.103113756 -1.77799849 -1.0931648334 -0.0122323381 -0.394650374
## [100,] -0.409442426 0.35492707 -1.0502000077 1.4204609639 -0.397600387
## [101,] 4.633190126 2.16526818 0.6239105977 -1.1366907435 0.716197325
## [102,] -0.740349810 1.21149156 -0.0348952140 -1.2669488699 0.172769662
## [103,] 0.704221402 -1.11279489 -2.7553374907 -0.4028612238 2.065387989
## [104,] -0.385204834 -0.52764189 -1.2886177272 0.4419425766 0.047208371
## [105,] -0.068793640 0.07508422 -0.6067830446 -0.3162015548 -0.041201539
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## [162,] -1.591129974 -0.30100995 -1.4737482868 -0.1586928611 0.631200467
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## [164,] -1.257058960 0.98743371 0.2695795040 -0.5173988569 -0.667657584
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## [166,] 0.763873736 -1.48595671 -1.3893183822 1.8933152957 -0.923231546
## [167,] -0.648233872 0.65902369 -0.3523707692 -0.3496173059 0.053036529
## [168,] 4.075761272 -0.02211354 1.3258187920 -1.7139363992 -0.985583605
## [169,] 0.108096807 -0.74362678 -1.3323697664 -0.3209218040 0.450579099
## [170,] -1.498040609 0.19056435 0.2761281170 -0.9725452192 -0.798104332
## [171,] 0.047885996 0.72229011 -0.4345521427 1.3431830404 -0.865118234
## [172,] 1.337596168 -0.99890019 -0.4764831468 1.0952509419 -1.281949522
## [173,] -1.358485537 -0.11022223 -0.3457867052 -1.0397848770 -0.109872739
## [174,] -1.872027381 0.13432597 -0.2581474106 0.2022369490 -0.831155436
## [175,] -1.311243234 1.36865781 0.6373415177 -0.4090917149 -1.011660986
## [176,] 1.309706033 -1.47375458 -0.5852915698 -1.0931889293 -0.278496918
## [177,] -0.190859319 1.67724390 -0.7080844449 0.4280689948 0.590243975
## [178,] -1.150520519 -0.39541176 -0.6403158755 -1.4507416448 0.354044928
## [179,] 1.562083350 2.47954880 0.2323943105 -0.3200123444 0.378480572
## [180,] 0.457663612 -0.14582329 -0.6638729701 0.7733241568 -0.509222553
## [181,] -1.138195339 2.01560621 0.8465374351 -0.4823983801 -0.986316252
## [182,] -0.007740653 0.82444862 -0.0002346095 0.3074323320 -0.807425073
## [183,] -1.442466409 0.10416344 -2.2744315999 1.2646597948 1.004394643
## [184,] 1.401099127 0.69145106 -0.3432001965 -0.4552169029 0.392406398
## [185,] 3.044609211 -0.84163842 0.2359688651 -0.0030339038 -1.095598605
## [186,] -0.608848019 0.10718396 -0.0234540132 0.6904571295 -1.303809693
## [187,] 0.869481448 -1.63077965 -0.5698543214 1.5434401088 -1.685405103
## [188,] -0.300778748 0.05603470 -0.4615545760 0.1636332520 -0.514773465
## [189,] 0.636747830 2.30234603 1.1644239379 0.0093990323 -1.179875943
## [190,] -1.117892469 0.18858115 -0.3253204166 -1.3032488160 0.106289330
## [191,] -0.433517740 -0.06760578 -0.8846842302 0.3292279071 -0.195203996
## [192,] -2.074508151 -0.53753951 -0.4998051808 -0.0243119417 -0.707539233
## [193,] -0.943857160 1.31427799 -0.3177697220 0.3467708448 -0.211477339
## [194,] -0.671437346 -1.01840193 -0.5258171064 -0.3862781611 -0.631526388
## [195,] 3.146400023 -0.15766658 -0.4540461596 -0.5782133325 0.335024707
## [196,] -1.646968799 0.07418381 -1.4456195095 0.8218169329 0.234350644
## [197,] 0.194381857 0.17982364 -0.8329361597 0.1578319644 0.012979177
## [198,] 1.355794604 -1.31217975 0.2126240281 -0.5341546811 -1.308712601
## [199,] 0.342080981 0.71442970 -0.6482593800 -0.2099015734 0.202983167
## [200,] -0.390007297 -0.72256040 0.2659366383 -1.3023370226 -0.917914031
## [201,] -0.278709707 -0.06166132 -0.3047482694 -0.2069801581 -0.550875712
## [202,] -0.042662340 0.49913934 -0.5186429497 0.4553285736 -0.344718375
## [203,] -1.773111892 -0.17830822 -1.7400026462 1.2398085147 0.256196652
## [204,] 1.250439359 1.30927635 -1.2548155696 0.1212141597 1.352914243
## [205,] -1.763032603 -0.39026215 -1.0709293305 0.7285468245 -0.342694606
## [206,] -1.734908122 0.22532626 -1.3096386361 1.1382811564 -0.036594174
## [207,] -0.040455138 0.55449852 0.4573444687 -0.4218347821 -1.104169327
## [208,] -0.686284826 0.13219155 0.6118547014 -0.2432679726 -1.594675721
## [209,] -0.444359734 -0.28370817 -0.4495876614 -0.0769292704 -0.578337456
## [210,] 0.691490501 -1.91894081 -0.1931803231 -0.7485897999 -1.218968830
## [211,] 2.007551495 -1.38730232 -0.5519627527 -0.6174453995 -0.374722131
## [212,] 2.980951104 0.35496999 -1.5634230702 -0.6219160971 1.802482148
## [213,] -0.051043670 1.76211010 1.2088357396 -1.1338711513 -0.589252139
## [214,] -1.433696923 0.30117834 -1.1167790798 0.7158629306 0.010513237
## [215,] 0.663189426 0.17003794 -0.7914480913 0.1781148795 0.204851463
## [216,] 2.031410016 -1.22967790 -2.3061777513 2.1455817946 0.319442130
## [217,] 0.789603453 -0.46930287 -1.7356512834 -0.3692602528 1.111404116
## [218,] 0.673484381 -0.39280224 0.0473568504 1.1650225109 -1.817685120
## [219,] -1.540903396 -0.09859304 -1.1167612805 0.8029841934 -0.165862050
## [220,] 4.811125983 2.34468196 -0.3322754239 0.5855998508 1.125323479
## [221,] 2.960210184 0.25580109 -1.3532023514 1.1105279220 0.660503185
## [222,] 0.548555090 1.20673516 -0.5847280068 1.2403006951 -0.255814803
## [223,] -1.203818787 0.41491335 0.6516018979 -1.7888960008 -0.675920517
## [224,] -0.095903547 -0.65584776 -0.5358363119 -1.2541542670 0.075096599
## [225,] -1.447284264 -1.00724102 -0.6082703522 -1.5298781643 0.066886767
## [226,] -0.721456172 1.13787970 0.8467912909 -2.0802276689 -0.435596218
## [227,] 2.040310983 0.43242568 -0.2461052925 0.7423873284 -0.579002419
## [228,] 1.855207556 1.67633604 0.5148301396 -0.1260125667 -0.807029471
## [229,] -1.362709085 0.28203522 -1.2055884775 0.5729921576 0.186353531
## [230,] -0.288896751 0.20730044 0.2845176632 0.6308919312 -1.505210536
## [231,] -0.418601999 0.23532480 0.2238988269 -0.5027334058 -0.945826637
## [232,] -1.163850583 0.68497750 -0.8821849871 0.8863377110 0.002177941
## [233,] 0.411132602 1.16486925 -0.3493614654 1.3942763398 -0.698315265
## [234,] -1.693135796 -0.47771445 -1.0852001549 0.2466849979 -0.106371453
## [235,] -1.469262447 0.58168692 0.2179103849 0.0730339108 -1.083523772
## [236,] -1.241804213 1.79930936 0.0417415503 0.6900290082 -0.739436237
## [237,] 3.689808324 1.67054618 0.2271980354 -0.1712036874 0.320606604
## [238,] 0.637785394 -1.18641596 0.3164064662 0.3364686684 -2.013280789
## [239,] 6.741912903 1.29247340 -0.5420542885 0.4573219426 1.094774796
## [240,] -1.238593026 -0.23776840 -0.5949271348 -1.3969869040 0.325843132
## [241,] 0.823175506 1.06316740 -0.5254541417 -0.6645444043 0.438143394
## [242,] 0.046147404 1.10794300 0.9541899343 -1.0517974932 -1.112030077
## [243,] -0.926653518 -0.47703938 0.3584883210 0.7483755808 -2.030451588
## [244,] 1.642861658 0.76706108 0.4101327315 -1.6601340760 0.241603918
## [245,] 0.577872627 -0.27228218 0.0857683853 -1.3777634787 -0.319784341
## [246,] -1.754825326 0.80791517 0.5577871077 -0.0676093662 -1.377625236
## [247,] -2.038325012 0.13688760 -0.0003412363 0.3430358578 -1.217973430
## [248,] 0.534102452 0.42078510 -1.1547081981 -0.6235503927 0.941303310
## [249,] -0.778602587 0.16187841 -0.3007337578 -2.1397103069 0.556468021
## [250,] -1.358620602 -0.11871598 -0.0786250759 -1.0668656351 -0.441391917
## [251,] 0.552972231 -1.32892174 0.2653874378 -1.7448134449 -0.716425820
## [252,] 0.160512695 -1.07401603 -1.3645629081 0.1229912862 0.139386122
## [253,] -0.255760964 -1.55052571 -0.6215940219 -1.4389507212 -0.116189564
## [254,] 2.380048532 -1.22313608 -0.4828668231 -1.7734074221 0.293324720
## [255,] 2.562080786 -0.62564376 -0.7980444051 1.7530531164 -1.022362433
## [256,] -0.556325503 0.61870762 0.4208116759 0.5833612102 -1.567526425
## [257,] -1.361977024 0.48557037 -0.3780687286 -0.2263198361 -0.261824026
## [258,] -1.604168388 0.15729081 -1.1427967214 0.6878894786 -0.014904788
## [259,] 0.453544197 -0.10135935 -0.0830135546 -1.4480142567 -0.154195510
## [260,] -0.245088734 -0.21116664 -0.8071754259 0.2429511311 -0.279436645
## [261,] -0.586494355 0.59713665 -2.4100725243 -0.5973150226 2.411185160
## [262,] -0.595783004 -0.97017702 0.1712856607 -1.4091442191 -0.895962157
## [263,] -0.098509308 -0.71157736 -0.6190102919 -0.8101660640 -0.107118411
## [264,] -1.732739711 -0.01171917 -0.9714345094 0.9911466978 -0.385416176
## [265,] -1.312518153 2.21664937 1.0466799279 0.0855880150 -1.449625633
## [266,] -1.117483636 -1.07344208 -0.1309504223 0.5351107892 -1.625027906
## [267,] -0.802242010 2.43916871 -0.0658918448 0.5326247945 -0.249856505
## [268,] 1.779574174 -2.20525734 -1.2254437217 -1.4601618621 0.480018703
## [269,] -0.692885384 -0.50625416 -1.6109602188 1.2266062367 0.002189829
## [270,] -0.296827034 2.09903244 -0.5356781950 1.0212095064 0.236744458
## [271,] 2.648459041 -0.60314173 -1.1623236353 -1.1868983731 1.137440016
## [272,] -0.009329958 0.66837011 -0.6089249244 -0.0124265699 0.007020687
## [273,] 0.636626889 0.36453000 -1.0956031271 -0.4201642118 0.755836178
## [274,] -0.730329225 0.63180054 -0.2775908413 0.0076169716 -0.174167360
## [275,] 0.329127497 -0.70211196 -1.1270499206 -1.3794822582 0.788719121
## [276,] -1.859016837 -0.41444458 -1.0884680056 0.0004891493 0.032889030
## [277,] 2.011187895 -1.86028031 -1.4701740451 1.9592818340 -0.863881329
## [278,] 4.387657320 1.01990704 -1.0694317529 1.0313056985 0.910287718
## [279,] -1.562200265 0.50506920 0.3257902808 0.4071536855 -1.418071805
## [280,] 1.140064695 -0.84165314 0.0475366423 0.1828157194 -1.383731574
## [281,] -1.592089421 0.68980851 0.0241838972 -0.0763303675 -0.781020214
## [282,] -0.863852065 0.20642081 -0.8983962803 -1.0667886017 0.713765183
## [283,] 1.027169030 1.16456255 -1.0404846287 -0.0396471898 1.049317709
## [284,] -0.436517354 -0.42713213 0.0134409058 -0.8973018413 -0.722139204
## [285,] 0.337411799 -0.24417082 -0.6480989722 -0.0855047074 -0.227110796
## [286,] 0.922063650 -0.22614793 -1.9443047687 0.7895315305 1.017821370
## [287,] 0.074518204 0.02674638 -1.0857966267 0.5553685803 0.035340926
## [288,] 0.517903752 0.07720678 0.7802091323 -0.3889323964 -1.326401252
## [289,] 1.205633993 4.05992941 1.7774871852 0.5243784073 -0.779237256
## [290,] 5.667322803 1.41683162 0.5192606886 -0.5242010735 0.057913957
## [291,] 0.117634314 2.05280704 1.1202906141 -0.2225732744 -1.394044856
## [292,] -1.257776898 0.99085451 -0.6432249171 0.7239870280 -0.267413061
## [293,] -1.442594978 0.64860803 -1.1825132672 1.3464166771 -0.103965971
## [294,] 0.581815447 0.15948370 0.5111637426 -1.5852378542 -0.514462082
## [295,] 3.192976367 -0.80514579 0.6934590185 -0.6145019682 -1.279398203
## [296,] -1.664428065 0.44940153 -0.8138817842 0.9169350091 -0.409961580
## [297,] -1.381280799 -1.04718836 -0.8104653996 -1.2130194950 0.131190811
## [298,] -0.359580844 -0.02707621 -0.2139147820 0.7519546558 -1.081305483
## [299,] -1.295214100 0.90633579 0.3446284016 -0.9705650257 -0.587847432
## [300,] 1.275367360 -0.46955884 -0.9321790556 1.6880185073 -0.857351331
## [301,] 0.510190648 -0.47545309 0.1659852525 -1.4398287570 -0.586650046
## [302,] 0.497692443 0.73632621 -0.7320867366 -0.6396358886 0.543145415
## [303,] -0.360524908 1.94049135 -0.0814679929 -1.0578009624 0.492777950
## [304,] 0.680162177 4.39853961 1.3939873156 -0.0903894719 -0.359689359
## [305,] 0.651993920 1.46566547 -0.5054646735 1.4206026417 -0.393377040
## [306,] 3.788964776 -1.08829199 -1.2835697130 1.5189289232 -0.160003180
## [307,] 0.324102302 0.44636919 -0.0358560470 -1.7147746806 0.185602167
## [308,] 1.241627938 -0.80113200 -0.9370602561 0.5736384332 -0.380036721
## [309,] -0.511968929 -1.17458566 -0.6546640582 -0.3823368294 -0.528559592
## [310,] 0.718039754 0.17733890 -0.6884966946 -1.2988653722 0.666658316
## [311,] -0.310163020 -1.06311682 -0.8411613032 -0.3440185709 -0.239649145
## [312,] -1.033055205 1.28803157 -0.7885399882 1.0583019502 -0.014148637
## [313,] -0.764852259 0.84975776 -0.4166580478 -0.3570104900 0.163850456
## [314,] 2.840965510 1.27703956 1.2737033558 -0.0712572107 -1.299150219
## [315,] -1.178758036 -0.07789715 -0.1547232721 -1.1892312531 -0.258297637
## [316,] -0.802177079 -0.95036649 -0.6926590212 0.0641135168 -0.653215774
## [317,] 1.938258838 -1.28408318 -0.7550485265 -0.2456973992 -0.386044302
## [318,] -1.084340607 0.56509571 -0.3641566428 -0.4657496728 -0.069947785
## [319,] 5.007927517 1.33213703 0.4628978606 -0.6412930066 0.335503981
## [320,] -0.352175349 0.05184295 -1.0595996323 1.1419351290 -0.354514092
## [321,] -1.645893870 0.67772347 0.5678664419 -0.6516041624 -1.130232840
## [322,] -0.723629619 0.28418574 -0.9155428645 -1.7398043966 1.090294733
## [323,] 2.150497872 -1.85335253 -0.9536747162 -0.9930159522 0.090967074
## [324,] 0.219479185 0.70653560 0.4625353948 0.0635989317 -1.095438714
## [325,] -0.347437994 0.13601327 -0.3616040070 0.0995137840 -0.602584780
## [326,] -0.234908136 0.38370796 0.3810829977 0.2955102824 -1.313248723
## [327,] 0.016559745 -0.24813137 0.3418529439 -0.6289931873 -1.073354029
## [328,] -1.467247701 -0.93657939 -1.0073778050 -1.3484920808 0.464904725
## [329,] 1.154836707 -1.65839860 -0.1796696786 0.5786916927 -1.773817068
## [330,] 0.020892606 0.14389944 0.1408600742 0.1842691926 -0.953519579
## [331,] 0.169022729 0.24173475 0.6782816134 -1.3801420819 -0.971815989
## [332,] 0.596241854 0.70051500 -1.8052088015 -0.0053918173 1.465700551
## [333,] -1.658882001 -0.32657130 0.2318064743 -0.3636469103 -1.209182254
## [334,] -1.130296134 0.92484749 -0.3380519552 -0.3013039197 -0.112208131
## [335,] -0.114349001 -0.27920208 -0.6403335111 -0.2074405468 -0.257747260
## [336,] -1.180178802 0.03183833 -0.3500656477 -1.0972084429 -0.005358715
## [337,] 1.016962553 -1.84125842 -1.0359966156 0.1725787385 -0.567197423
## [338,] 1.874901202 -1.13532877 -0.6093993174 1.0930613053 -1.160229327
## [339,] -1.674481841 0.44986836 2.1646104925 0.9678148811 0.135461099
## [340,] 0.347838749 -0.88857174 0.8771393702 -0.0399280185 1.772672225
## [341,] -0.523787799 -0.92658682 1.5418929659 0.1325485002 0.785980424
## [342,] -1.191298001 1.23405600 1.7890495622 1.3692564275 0.892653715
## [343,] 1.808772263 -1.69685692 0.8907964331 -0.2029722962 1.489618576
## [344,] -1.770065768 -0.81617964 1.3539885104 -0.2766980579 1.166492368
## [345,] -0.206433118 0.56197089 1.8053747930 1.3814075643 0.495893161
## [346,] 0.781356058 -0.26730308 1.4981375832 0.8043655618 1.134248369
## [347,] -1.821829245 -1.41978625 1.5929954355 -0.6929508188 0.865846962
## [348,] -0.284787326 -0.98055909 2.0711730642 -0.3625595662 0.392274537
## [349,] -0.436832085 1.81979653 1.9654352950 0.0409412675 1.657960929
## [350,] -1.217940564 -0.03242505 1.5341269350 0.0689673368 1.157904466
## [351,] 1.408443279 -0.92755403 2.5527909101 -0.6932672647 0.150225917
## [352,] 0.076806137 -0.36230781 1.0569801425 0.7081503355 1.356282603
## [353,] -1.371613972 -0.73826316 -0.0390647200 0.5827617423 2.417181597
## [354,] -1.864312777 -1.17836386 1.6190160585 -0.8239266507 0.990897877
## [355,] -1.989259900 -1.78295952 1.5112558257 -0.6883823148 0.805384073
## [356,] -0.666931670 0.04442279 0.9603229118 1.9679277491 0.821582895
## [357,] -0.752021652 0.57932223 1.1919215542 0.0297044937 1.852331941
## [358,] -0.799705965 -1.07103612 0.3748144882 2.1390626788 1.010092176
## [359,] -1.601727166 -1.41026284 0.7915067164 -0.2584759327 1.601877583
## [360,] -1.657122757 0.50517962 1.7207936026 1.3778309508 0.405279647
## [361,] -0.384493964 -0.88081329 0.5179378168 0.9525680456 1.560400572
## [362,] -1.117824446 0.07013439 2.3329630062 -0.8981794794 0.738754653
## [363,] 2.156938592 -0.59054334 0.9679981313 1.4564801625 1.063503699
## [364,] -0.789754021 -2.12761614 1.4729430325 0.0219314842 0.410727684
## [365,] -1.380570918 -1.02926654 1.9974600705 -1.3875631548 0.968366183
## [366,] -1.291560292 0.38334086 1.4160677141 1.5258026469 0.762317564
## [367,] -0.935262338 0.56231264 2.1242791830 0.3720182728 0.718006182
## [368,] 2.492171120 -0.48928746 2.4676282836 1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614 2.2688783371 0.9603180211 -0.407816836
## [370,] -1.468296601 0.18028669 1.6652393313 1.5773153771 0.412661443
## [371,] 0.644477407 1.35334644 2.6883609615 0.5712489712 0.440528158
## [372,] 4.369563022 -1.66481832 1.6865361527 0.4901972904 0.760040778
## [373,] -2.357052820 -1.26900605 1.5231357317 1.0301102498 0.074632682
## [374,] 0.718708019 0.22127710 1.0354060443 0.2583339391 1.891779073
## [375,] 1.391878059 0.98004221 1.7111474295 -0.7952838709 2.265775349
## [376,] 0.905097897 -0.22694710 2.1140189340 0.5476029310 0.603860387
## [377,] 3.157230391 -1.19754195 1.1484347290 1.0599855046 1.186962665
## [378,] 0.003135705 -0.90598915 1.6393299343 -1.1011824448 1.359035590
## [379,] -0.242056357 -0.73255189 1.7021620290 -0.1866470103 0.800865246
## PC6 PC7
## [1,] 0.814428206 -0.107883916
## [2,] -0.048912344 -0.099604504
## [3,] -0.086507916 -0.138527863
## [4,] -0.822748232 0.360506834
## [5,] -0.108812986 0.078970882
## [6,] 0.183797925 0.433343571
## [7,] 0.008911379 -0.004657966
## [8,] 0.543125568 -0.332707934
## [9,] -0.752701863 0.056474342
## [10,] -0.441826427 -1.924448799
## [11,] -0.244944687 0.159851097
## [12,] 0.206259597 -0.169273224
## [13,] 0.163519054 -0.103667561
## [14,] 0.132474346 0.108653816
## [15,] -1.324055932 -0.183915616
## [16,] 0.714919089 0.304537991
## [17,] -0.647376538 0.365592105
## [18,] 1.097596271 -0.377715183
## [19,] 0.334391075 -0.234827285
## [20,] 0.808587321 -0.200036177
## [21,] 0.322170368 -0.166529357
## [22,] 0.107803508 0.012805983
## [23,] -0.332323319 -0.202474142
## [24,] 0.995998868 0.201016672
## [25,] -2.363493528 0.266625584
## [26,] -0.813907073 -0.571488560
## [27,] -2.160783056 0.281527887
## [28,] 0.098479393 0.336756957
## [29,] 0.004273460 -0.381406184
## [30,] -0.044211599 -0.418300721
## [31,] -0.128464996 0.054899611
## [32,] -0.357344175 0.183909490
## [33,] -0.597244606 0.289672968
## [34,] 0.259235600 0.349194654
## [35,] -0.236888897 -0.371166651
## [36,] -0.249251785 0.050335461
## [37,] 0.607590347 -0.462113845
## [38,] -0.026797156 0.355817879
## [39,] 0.166045669 -0.073826942
## [40,] -0.162738506 -0.392300116
## [41,] -0.522507663 -0.121724380
## [42,] 0.067225848 0.209115377
## [43,] -0.417780877 -0.474060203
## [44,] -0.173878940 -0.457967209
## [45,] -0.050403121 -0.134114068
## [46,] -0.089979747 -0.491479393
## [47,] 0.480573605 -0.072323181
## [48,] 0.228887831 0.155522234
## [49,] -0.489991807 -0.227097997
## [50,] -0.606582969 -0.101166456
## [51,] 0.577660866 -0.455756839
## [52,] 0.585446120 -0.388137976
## [53,] 0.734811073 1.561539615
## [54,] 1.381511548 0.252947237
## [55,] 0.358959045 -0.182311216
## [56,] 0.207910788 0.078632864
## [57,] 0.607774154 -0.281869942
## [58,] 2.443161543 0.443513680
## [59,] 0.206843192 0.253038172
## [60,] 0.135499206 0.164773439
## [61,] 0.648725932 0.351461678
## [62,] 0.166486526 0.246682271
## [63,] -0.513948300 -0.286040883
## [64,] 1.163578265 0.263125274
## [65,] -0.009862807 0.134046265
## [66,] -0.730377136 0.337181681
## [67,] -1.487448857 -0.149925371
## [68,] 0.220853759 0.272493773
## [69,] -0.588054260 0.260689981
## [70,] -0.385273067 0.319508713
## [71,] -0.175254751 1.897246402
## [72,] -1.300330063 -0.404208363
## [73,] 0.816322549 -0.225387244
## [74,] -0.060212427 0.165026305
## [75,] -1.649589162 -0.529795744
## [76,] 0.569158827 -0.263377372
## [77,] -0.165692949 -0.401192949
## [78,] 0.043436354 0.440699177
## [79,] 0.327782857 0.371732847
## [80,] 0.016945132 0.140928440
## [81,] -0.877693420 -0.271276638
## [82,] 0.050656761 0.314869348
## [83,] 0.024270266 -0.489647178
## [84,] -0.428408376 0.144447332
## [85,] 0.302353058 0.176709283
## [86,] -0.930367776 -0.038966156
## [87,] 0.206974359 1.518547012
## [88,] 0.773220076 0.387655208
## [89,] -0.057425863 0.311702214
## [90,] -0.319492539 -0.104439493
## [91,] 0.464021241 -0.182053564
## [92,] 0.568469956 0.135273025
## [93,] -0.637098352 -0.352179961
## [94,] -0.897710356 -0.603436508
## [95,] -0.302718373 0.134220300
## [96,] 0.796303291 -0.453234619
## [97,] 0.102248374 -0.373850042
## [98,] 0.276775028 -0.386841666
## [99,] -0.147547074 -2.150145655
## [100,] 0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,] 0.945355253 0.288290374
## [103,] 0.240503118 0.089283023
## [104,] 0.040655927 -0.326527188
## [105,] 0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,] 0.617517671 -0.018331347
## [108,] -0.140360458 0.357139007
## [109,] -0.369058053 -0.363453154
## [110,] 1.367651547 -0.052494633
## [111,] -0.245674045 0.171961839
## [112,] -0.288279169 -0.437854120
## [113,] 0.654181743 0.335734007
## [114,] 0.430171258 0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461 0.293451739
## [117,] 0.435961104 0.348338090
## [118,] -1.122876095 0.371334968
## [119,] 0.128953459 -0.002950892
## [120,] 0.454338848 -0.320002000
## [121,] -0.393321862 0.002244332
## [122,] 0.694427666 -1.776651924
## [123,] -1.480360092 0.237363812
## [124,] 0.563305776 0.061168635
## [125,] 0.789672355 0.182676841
## [126,] 0.657430786 0.151394277
## [127,] 0.052053042 -0.260063201
## [128,] -0.509971776 0.300299579
## [129,] -0.514688913 0.253498821
## [130,] -0.230653718 0.334001823
## [131,] 0.234492897 0.070164155
## [132,] -0.509623760 0.211476411
## [133,] -0.508032972 0.218820879
## [134,] -0.584676128 0.432040803
## [135,] -0.599512631 0.114578050
## [136,] 0.742555446 0.264941606
## [137,] 0.215593238 -0.296341138
## [138,] 0.814373445 -0.463329220
## [139,] -0.705236433 0.235224585
## [140,] -0.240819937 0.128832004
## [141,] -0.738265473 0.045748305
## [142,] -0.516065685 0.423763629
## [143,] 1.032627703 0.255695270
## [144,] 1.011640901 -0.046612704
## [145,] 1.036057364 -0.116502648
## [146,] 0.238779557 -0.094409829
## [147,] 0.093045275 -0.025943269
## [148,] -0.018285774 0.063985702
## [149,] -0.821062597 0.316957388
## [150,] -0.051433159 -0.325889337
## [151,] 0.240258258 0.157499206
## [152,] 0.244055313 -0.484326189
## [153,] 0.321762278 0.347844280
## [154,] -0.688031620 0.275674116
## [155,] 0.052870105 0.278750325
## [156,] 0.259394959 0.994613529
## [157,] 0.384573263 0.255112420
## [158,] -0.647167228 0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,] 0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636 0.354791023
## [164,] 0.259528832 0.196856471
## [165,] -0.112837907 -0.422270866
## [166,] 0.128000241 -0.175939627
## [167,] -0.895512404 0.337192272
## [168,] -0.711019273 -0.814804273
## [169,] 0.218357219 -0.033915231
## [170,] -0.078144315 0.263676922
## [171,] 0.789052948 0.069697557
## [172,] 0.334044498 0.095799549
## [173,] -0.466799910 0.182242801
## [174,] -0.409218588 0.105315011
## [175,] 0.475675622 0.157100174
## [176,] 0.631970192 -0.312887516
## [177,] -0.842796008 0.184336624
## [178,] -0.521271064 0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439 0.339455192
## [181,] 1.224469205 0.162311433
## [182,] 0.896759582 -0.187133556
## [183,] -0.369525579 0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790 0.938668397
## [186,] 0.115704613 -0.308573611
## [187,] -0.330011041 0.052298230
## [188,] 0.252831722 -0.344500770
## [189,] 0.478267892 -0.411989559
## [190,] 0.108389410 0.270176494
## [191,] 0.320051815 -0.452948617
## [192,] -0.927317654 0.050049377
## [193,] 0.049967323 0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643 0.112196595
## [196,] -0.426323754 0.064708147
## [197,] 0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,] 1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,] 0.222523935 -0.327353336
## [202,] 0.143637470 -0.384469784
## [203,] -0.685873899 0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209 0.286336764
## [206,] -0.391145161 0.071275723
## [207,] 1.031184262 -0.071523474
## [208,] 0.422795216 -0.361912372
## [209,] 0.232252275 -0.321891385
## [210,] 0.132512399 -2.194006418
## [211,] 0.300407101 0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275 0.013076856
## [214,] -0.146543860 0.258375350
## [215,] -0.914443039 -0.156858207
## [216,] 0.163052914 0.373094641
## [217,] 0.735902331 0.298434341
## [218,] 0.858016687 -0.410620478
## [219,] -0.698483214 0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,] 0.103014117 -0.154551366
## [223,] 0.032313480 0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311 0.316447811
## [226,] 0.757677018 0.355289619
## [227,] 0.112343498 -0.370694673
## [228,] 2.840081863 -0.472760040
## [229,] -0.117535015 0.251369052
## [230,] -0.123999729 -0.103219333
## [231,] 0.620151206 -0.398726087
## [232,] -1.258499518 0.031686285
## [233,] 0.508788077 0.031702502
## [234,] -0.730990134 0.229897436
## [235,] -0.131943879 0.351750927
## [236,] 0.930178961 0.218030323
## [237,] -1.155883577 -0.406938969
## [238,] 0.421016873 -0.245001577
## [239,] -0.919968833 0.339656927
## [240,] -0.475488496 0.136247856
## [241,] 1.761754259 0.029538972
## [242,] 1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019 0.116533237
## [246,] 0.123274608 0.151123503
## [247,] -0.489960306 0.098338159
## [248,] 0.676566199 -0.339944716
## [249,] 0.072286130 0.262572292
## [250,] -0.203974262 0.359934672
## [251,] -0.962511140 0.447744836
## [252,] 0.026617023 0.293556296
## [253,] -0.615601226 -0.158798853
## [254,] 0.165313198 0.013008846
## [255,] 1.432136191 1.223639292
## [256,] 0.483977624 -0.346520349
## [257,] -0.153805545 0.159416002
## [258,] -0.327177547 0.145372443
## [259,] 0.927279628 0.136024542
## [260,] 0.347645497 -0.209884830
## [261,] 0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891 0.117204649
## [265,] 1.233710972 0.172803485
## [266,] -0.621049559 -0.266818669
## [267,] 1.556396291 0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685 0.155867363
## [271,] -0.136040334 -0.327359471
## [272,] 0.778990215 -0.465309183
## [273,] 0.693723928 -0.130197667
## [274,] -1.468695169 0.266972231
## [275,] 0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,] 0.336674762 1.064820895
## [278,] -0.300804152 0.703841870
## [279,] -0.238262975 0.450690335
## [280,] 0.395969716 -0.242043012
## [281,] 0.109021256 0.138748544
## [282,] -0.037963898 0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,] 0.426625104 0.228719436
## [286,] -0.362288537 0.223311049
## [287,] 0.384277844 -0.106878993
## [288,] -1.421668738 0.046595855
## [289,] -2.984199195 0.075859453
## [290,] 1.319916883 2.001667923
## [291,] 2.046793198 -0.269649215
## [292,] 0.392813424 0.303644436
## [293,] 0.021688217 0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153 0.163389864
## [297,] -0.811118093 0.416648260
## [298,] -0.340865035 -0.224224889
## [299,] 0.466059600 0.157785884
## [300,] 0.558304051 -0.192471657
## [301,] 0.750653613 0.459663166
## [302,] 1.122352945 -0.276052847
## [303,] 1.078964668 0.210264826
## [304,] 0.426300512 0.141513828
## [305,] 0.810547774 0.065859782
## [306,] -0.181814543 1.697357273
## [307,] 0.699571022 -0.449062901
## [308,] 0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,] 0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323 0.125575320
## [313,] -0.600269847 0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717 0.438769076
## [316,] -0.386407008 -0.406110560
## [317,] 1.041640267 0.390303651
## [318,] -0.189857024 0.234508553
## [319,] -1.090183460 0.762300322
## [320,] 0.386282802 -0.239807387
## [321,] 0.134404520 0.127105246
## [322,] 0.366835108 0.216268360
## [323,] 0.342909111 0.372677157
## [324,] -0.254516438 -0.193658003
## [325,] 0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346 0.003333250
## [328,] -0.798713796 0.164392019
## [329,] 0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,] 1.020308661 0.044230674
## [332,] 1.056394345 -0.394589336
## [333,] -1.007313550 0.374213944
## [334,] 0.492601789 0.244276984
## [335,] 0.411613111 -0.135788109
## [336,] -0.280767946 0.263720304
## [337,] 0.160862506 -0.192753984
## [338,] 0.791036742 0.678047807
## [339,] 0.126529280 0.120748763
## [340,] 0.262317102 -0.088849352
## [341,] 0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,] 1.445310485 0.036985630
## [344,] -0.175915279 0.027902348
## [345,] 0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184 0.213624141
## [348,] 0.448319463 -0.109057231
## [349,] 0.164185074 -0.178027089
## [350,] 0.343302649 0.295711308
## [351,] 1.064600476 -0.399557062
## [352,] 0.402428026 -0.264910522
## [353,] -0.039235833 0.080955691
## [354,] -0.401278508 0.033682397
## [355,] -0.845062983 0.190359077
## [356,] 0.916027349 -0.545821754
## [357,] 0.946629462 0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729 0.232244290
## [360,] 0.620269650 0.217072532
## [361,] 0.290272477 -0.446292100
## [362,] 0.807055770 0.427223893
## [363,] 1.725250067 0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260 0.310782840
## [366,] -0.025556816 0.310309937
## [367,] -0.369535370 0.246732337
## [368,] 0.794924538 0.929445109
## [369,] -0.044906053 0.144701045
## [370,] -0.730353345 0.202922032
## [371,] 0.105639703 -0.429239913
## [372,] -0.245135971 0.186120856
## [373,] -0.823120736 0.174853047
## [374,] 1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214 0.135743929
## [377,] -0.299503313 0.743333133
## [378,] 0.410392839 -0.361555114
## [379,] 0.837670932 -0.196874004
# Identifying the scores by their survival status
sparrtyp_pca <- cbind(data.frame(Cancer$Survivor),Cancer_pca$x)
sparrtyp_pca
## Cancer.Survivor PC1 PC2 PC3 PC4
## 1 Alive -1.441559363 1.84595445 -0.3691842456 0.8313546497
## 2 Alive 0.466697152 0.06803649 -0.6236808487 -0.3679040103
## 3 Alive 1.724644704 -0.46933933 -0.1593826887 0.5351088884
## 4 Alive -1.727412749 -0.67153366 -0.6471303735 -0.0657071859
## 5 Alive 0.084534880 -1.24252757 -1.5702796993 -0.3040439925
## 6 Alive -0.987174108 0.58301426 0.1669091720 -0.9999683133
## 7 Alive -1.289312885 0.33343114 -1.1225709379 -0.4660831193
## 8 Dead 0.457476281 -0.43703336 -2.3348237400 -0.5798103154
## 9 Alive 5.013544810 -0.35127563 0.3138865965 -0.6789485742
## 10 Alive 1.966110970 0.57900951 0.8436785098 1.1971488330
## 11 Dead -1.709742154 0.39272616 -0.8797546127 1.0395229446
## 12 Alive 1.323214712 -1.40692828 0.0010448762 -0.8532983622
## 13 Alive -0.047344848 0.20982069 -0.8615166802 1.1288786920
## 14 Alive -0.023379894 1.83512622 -0.8543600804 -0.5919635549
## 15 Alive 1.042993427 1.19479846 -0.1106365956 0.7578922926
## 16 Alive -0.954171084 1.25373181 -0.8631921253 0.4922727293
## 17 Alive -0.510183493 -1.74284660 -0.1083044907 -0.2184460954
## 18 Alive 0.248390384 0.43156365 -0.4623851738 -1.2333483190
## 19 Alive -0.386424810 -0.37494859 0.5477775527 -1.3442739171
## 20 Alive -0.212235416 0.44848661 -0.0814638947 0.1978257208
## 21 Alive 0.001291199 -0.22401731 -0.1753398416 -0.9042251252
## 22 Alive 0.547237523 0.35323566 -0.8945832960 0.4857434118
## 23 Alive -0.581794885 -1.07033107 -0.7283097731 -0.0629010628
## 24 Alive 1.484574719 -1.12275223 0.4930197218 -0.8534326311
## 25 Alive 0.730385134 3.01009366 1.5328340955 -0.0845516282
## 26 Alive 1.384044724 2.86730858 0.7935319092 0.4879719811
## 27 Alive 2.503197607 1.86942247 1.6035708576 -1.0898911376
## 28 Alive -1.094732396 0.13919430 -0.2430526831 -1.3348711724
## 29 Alive -0.040233637 0.24894946 -0.5823916977 0.1870202613
## 30 Alive -0.913495245 -0.27255918 -0.2249052502 0.7136559763
## 31 Alive 0.044817272 -1.24749459 -1.5147400984 -0.3403352312
## 32 Alive -1.310023914 -0.18810081 -1.5041631045 -0.0748728835
## 33 Alive -1.750326793 -0.31441971 -0.3126381565 -0.1365620557
## 34 Alive -0.860691537 1.17774354 -0.4731321013 0.2383866081
## 35 Alive 1.293140200 1.12837700 -1.0955034983 -0.3513923420
## 36 Alive -1.575412171 -0.65517742 1.1178980897 -0.0145585733
## 37 Alive 0.505620687 0.48204717 0.6768751198 0.9826148200
## 38 Alive -1.445729993 -0.53420180 2.0397881463 -0.4191403509
## 39 Alive -0.240634131 -1.38008841 1.2981310791 0.0234566336
## 40 Alive -0.335231355 -0.71567154 2.2622815166 -0.2598837684
## 41 Dead 2.392046521 -0.75381886 0.6808155988 1.7849935943
## 42 Alive -1.496209472 -0.05147919 0.8362058172 1.4463882147
## 43 Alive -1.238156754 -1.73396163 1.0838915624 1.1966166369
## 44 Alive -0.122858339 -0.41520397 1.7259286489 0.2467343049
## 45 Alive -1.614959830 -0.21262796 0.8270352673 0.5084458503
## 46 Alive 0.653344872 -1.45282335 1.6923961454 1.7730389364
## 47 Dead -0.903132282 0.00288121 0.2891894480 -0.3828977838
## 48 Alive -1.570956435 -0.13307164 0.7378711359 1.2691205943
## 49 Alive 0.407142180 -0.18484286 1.8224576827 0.3406571927
## 50 Alive -2.095133885 -0.24603762 1.3075254314 1.5865972660
## 51 Alive 0.145196356 -0.72051716 1.2885099274 -1.1072761596
## 52 Alive 0.438754344 -1.67207421 0.9831353778 2.3512915236
## 53 Alive 2.005777230 -2.95342227 1.2688959631 1.7356814675
## 54 Alive 1.526981600 -1.02119752 1.4223445513 1.8001650835
## 55 Alive -1.762004433 0.13389155 1.3060891880 0.4365138287
## 56 Alive -1.584099552 -0.27233552 1.1461680461 0.3643457178
## 57 Alive -0.496130040 0.33490544 0.2711418287 0.1648088615
## 58 Alive -0.310631363 3.07311289 1.8743230894 -1.7983452746
## 59 Alive -1.133478035 0.41599332 -0.4379284603 -0.8528069490
## 60 Alive -1.203472671 0.78226143 -0.1914939617 -0.4844823758
## 61 Alive -0.899762531 1.31926126 0.1811318594 -0.4938217806
## 62 Alive -1.006446958 0.35539993 -1.2221294160 -0.3469217710
## 63 Alive -0.437812701 -1.58636590 -0.8897438306 -1.2595916576
## 64 Alive 1.712300783 -0.45593265 -0.1013381728 0.5911078860
## 65 Dead -1.263885916 1.17224839 -0.6291534095 0.9206949813
## 66 Alive -1.604219653 -0.82712464 0.0494208809 -1.5797529143
## 67 Dead 4.488026052 1.14176192 -0.1231038156 -1.5112898673
## 68 Alive -0.665172931 0.68451038 0.1453995807 -2.0258292592
## 69 Alive -1.668377900 -0.33091730 -0.6606673180 -0.0526400595
## 70 Alive -1.130422629 0.23695569 -0.1769384999 -0.7612337767
## 71 Alive 3.316812797 -1.81535426 0.5502180418 -0.2694003925
## 72 Dead 2.172380940 2.85911092 -0.9844345887 1.6403461146
## 73 Alive 0.572326326 -0.34757898 -1.0234096521 -2.0869344002
## 74 Alive -1.827615023 0.62057292 0.3016558087 0.2426806849
## 75 Alive 0.720276568 1.70219107 0.6872975038 0.8005007414
## 76 Alive 0.849193077 -1.14260361 0.1217975270 -0.0272015985
## 77 Alive -0.640547040 -0.61272303 1.3854969929 1.5959470836
## 78 Alive -0.095120639 -2.25942107 1.7743414136 -0.8570595769
## 79 Alive -0.045215749 -1.67214619 1.1930256589 0.3311124134
## 80 Alive -1.769164273 -0.22777378 0.5215512977 1.9330657865
## 81 Alive 0.718379560 0.42702578 2.7049430509 0.0009902972
## 82 Alive -1.678008963 -0.30727716 0.8345249461 1.7090923528
## 83 Alive -0.895860760 -0.84819969 1.0351097886 1.6955225348
## 84 Alive -1.627068924 -1.17405222 0.1883777552 0.6241466387
## 85 Alive -1.331489281 -0.34160016 0.9121167916 0.1344506975
## 86 Alive 0.909892498 -0.53731582 1.4060161653 -0.0311065615
## 87 Alive 2.680823986 -2.87516871 1.2736995009 0.6959415006
## 88 Alive 1.353531002 -2.37316783 1.3254482077 0.7127875562
## 89 Alive -1.678967186 -0.70552936 1.6695940259 0.1038284595
## 90 Alive -2.304099591 -0.48981820 1.6210427235 0.9780934643
## 91 Dead 0.741204117 -2.34543537 1.4452706433 0.5998522096
## 92 Alive -0.809147683 -0.48805441 0.7203787577 -1.4686194537
## 93 Dead -0.790428226 -1.28394744 1.3498973595 1.2856985141
## 94 Dead 1.549314451 1.05942412 1.1109895492 0.1457696503
## 95 Alive -1.647991336 -0.27927996 1.6891990873 0.5048525410
## 96 Alive -0.268121798 -0.13194343 0.7385162603 1.3684964706
## 97 Dead -0.103534223 -1.33945241 -0.5191543874 1.0167737783
## 98 Alive -0.776307350 -0.99454099 1.0504553950 1.2109563269
## 99 Dead 1.103113756 -1.77799849 -1.0931648334 -0.0122323381
## 100 Alive -0.409442426 0.35492707 -1.0502000077 1.4204609639
## 101 Dead 4.633190126 2.16526818 0.6239105977 -1.1366907435
## 102 Alive -0.740349810 1.21149156 -0.0348952140 -1.2669488699
## 103 Alive 0.704221402 -1.11279489 -2.7553374907 -0.4028612238
## 104 Dead -0.385204834 -0.52764189 -1.2886177272 0.4419425766
## 105 Alive -0.068793640 0.07508422 -0.6067830446 -0.3162015548
## 106 Alive -0.692576410 -0.91636560 -1.3471231484 0.7054513599
## 107 Dead 0.345220609 -0.15476507 -1.9375149484 0.6213467649
## 108 Alive -1.364096376 0.64909093 -0.7204212843 1.0498159217
## 109 Alive -0.387521866 -1.16290394 0.1995560232 -2.1751452860
## 110 Alive 0.491580932 1.59726077 -0.0288299149 0.6365139827
## 111 Alive -1.087373932 0.96622658 -0.4850478973 0.2957151405
## 112 Dead 1.210180885 -2.10091879 -0.7122063654 -1.4443151802
## 113 Alive 1.869006469 1.83583553 0.7046224722 -1.0701872221
## 114 Alive 0.492734252 -0.45633393 -0.5614007104 -0.8951702764
## 115 Alive 0.889433533 -1.50731469 0.2004002058 -0.2364464439
## 116 Alive -0.849321798 0.50645649 -1.0584322308 -0.1780669707
## 117 Alive 1.382626614 -1.86070361 -0.1224339395 -0.3673855944
## 118 Alive -0.876114257 1.31244321 0.5402724456 0.6865577157
## 119 Alive 0.129510618 -0.29073195 0.1371234823 -1.0140234437
## 120 Alive 0.006142764 0.12672993 -0.8224846986 -0.0976817279
## 121 Alive -0.669636518 -0.67017693 -0.0910644210 0.8278709329
## 122 Alive 1.757579745 -1.15217572 -0.1806146788 -1.0023054945
## 123 Alive 1.875711497 0.92049908 -0.1305383937 -0.2267912179
## 124 Alive 0.312604564 0.73821191 0.3983729256 0.0063600881
## 125 Alive -0.681074580 1.46363098 -0.7243706847 -0.3192569625
## 126 Dead -0.863182056 1.24685123 -1.9912585523 1.1497711812
## 127 Alive -0.118572831 -0.70053670 0.2417380654 -2.0356708316
## 128 Alive -1.423953866 -0.28566927 -1.5423434161 0.5267774639
## 129 Alive -1.441335172 -0.03524627 -0.5051970790 -0.2755060729
## 130 Alive -0.856545337 0.21574546 -0.3501704930 -1.3208020069
## 131 Alive -1.307398005 0.79423090 -1.0835136941 0.4150931199
## 132 Alive 0.585398503 -0.41679342 -0.4499848326 -0.4042504411
## 133 Alive -1.786207788 -0.17673804 -0.0665424655 -0.3670738391
## 134 Alive -1.427017695 -0.63688709 -0.4649731902 -0.8892591027
## 135 Dead 0.756062138 -0.13112369 -1.3636990615 0.5752861401
## 136 Dead 0.145449916 1.69976295 -0.3153802001 -1.9246355296
## 137 Alive -0.274324587 -0.57433529 -0.2583518619 -1.1336704462
## 138 Dead -0.438129117 0.74050108 -0.3404267839 0.7633673055
## 139 Dead 1.064299809 0.61136855 -0.6550235320 0.9211144934
## 140 Alive 2.098096298 -0.42706015 0.8620866598 -0.4563567888
## 141 Alive -1.849943605 -0.47094945 -0.5180573283 -0.5701157634
## 142 Alive -0.732556857 -0.13070679 0.3510392562 -2.5238550573
## 143 Alive -0.608595125 1.35155467 -0.7057542462 -0.7165766057
## 144 Dead 0.505611656 1.09999711 -0.8457725436 0.9361832967
## 145 Dead 0.247551976 0.46673882 -0.7913160371 0.0399880240
## 146 Alive -0.602802743 -0.23260921 0.5437161698 -0.0788003168
## 147 Alive -1.272341157 0.63788399 0.2396679916 -1.6177473606
## 148 Dead 2.651497970 -0.83742214 -0.8602918415 -0.9187276925
## 149 Alive -1.824221268 -0.45358497 -1.0788845841 0.9216453730
## 150 Alive -0.352147008 -0.02439510 -0.1582340020 0.1140579142
## 151 Alive -1.129437762 0.24550127 0.4252415970 -2.4757263934
## 152 Alive -0.549974224 0.36383145 -0.6269521199 1.0856493132
## 153 Dead -1.104925141 0.73145555 -0.9068622646 0.3853904201
## 154 Alive -1.260493668 0.67356911 0.3950426508 -0.1537212632
## 155 Alive -1.263788087 0.89343258 -0.8613170835 1.0342322348
## 156 Alive 2.182293451 -0.70621431 0.3489551723 1.5351765574
## 157 Alive -0.839030427 0.51161725 -1.0551051340 -0.7935641661
## 158 Alive -1.567211240 -0.76592187 -0.0382695651 -2.2426462201
## 159 Alive -0.656681669 -1.17053344 -1.0085651375 -0.1509452878
## 160 Dead 1.746317858 1.20029090 -1.6249506696 0.9407644883
## 161 Alive 0.576848393 1.03248254 -1.8769456788 1.1403757019
## 162 Alive -1.591129974 -0.30100995 -1.4737482868 -0.1586928611
## 163 Alive -1.734769097 -0.63230165 -0.6993991424 0.0578306174
## 164 Alive -1.257058960 0.98743371 0.2695795040 -0.5173988569
## 165 Alive 0.171012852 0.73662045 -0.6335336460 0.6662455703
## 166 Alive 0.763873736 -1.48595671 -1.3893183822 1.8933152957
## 167 Alive -0.648233872 0.65902369 -0.3523707692 -0.3496173059
## 168 Alive 4.075761272 -0.02211354 1.3258187920 -1.7139363992
## 169 Alive 0.108096807 -0.74362678 -1.3323697664 -0.3209218040
## 170 Alive -1.498040609 0.19056435 0.2761281170 -0.9725452192
## 171 Dead 0.047885996 0.72229011 -0.4345521427 1.3431830404
## 172 Alive 1.337596168 -0.99890019 -0.4764831468 1.0952509419
## 173 Alive -1.358485537 -0.11022223 -0.3457867052 -1.0397848770
## 174 Alive -1.872027381 0.13432597 -0.2581474106 0.2022369490
## 175 Alive -1.311243234 1.36865781 0.6373415177 -0.4090917149
## 176 Alive 1.309706033 -1.47375458 -0.5852915698 -1.0931889293
## 177 Dead -0.190859319 1.67724390 -0.7080844449 0.4280689948
## 178 Alive -1.150520519 -0.39541176 -0.6403158755 -1.4507416448
## 179 Alive 1.562083350 2.47954880 0.2323943105 -0.3200123444
## 180 Dead 0.457663612 -0.14582329 -0.6638729701 0.7733241568
## 181 Alive -1.138195339 2.01560621 0.8465374351 -0.4823983801
## 182 Dead -0.007740653 0.82444862 -0.0002346095 0.3074323320
## 183 Dead -1.442466409 0.10416344 -2.2744315999 1.2646597948
## 184 Alive 1.401099127 0.69145106 -0.3432001965 -0.4552169029
## 185 Alive 3.044609211 -0.84163842 0.2359688651 -0.0030339038
## 186 Alive -0.608848019 0.10718396 -0.0234540132 0.6904571295
## 187 Alive 0.869481448 -1.63077965 -0.5698543214 1.5434401088
## 188 Alive -0.300778748 0.05603470 -0.4615545760 0.1636332520
## 189 Dead 0.636747830 2.30234603 1.1644239379 0.0093990323
## 190 Alive -1.117892469 0.18858115 -0.3253204166 -1.3032488160
## 191 Alive -0.433517740 -0.06760578 -0.8846842302 0.3292279071
## 192 Alive -2.074508151 -0.53753951 -0.4998051808 -0.0243119417
## 193 Alive -0.943857160 1.31427799 -0.3177697220 0.3467708448
## 194 Alive -0.671437346 -1.01840193 -0.5258171064 -0.3862781611
## 195 Alive 3.146400023 -0.15766658 -0.4540461596 -0.5782133325
## 196 Alive -1.646968799 0.07418381 -1.4456195095 0.8218169329
## 197 Alive 0.194381857 0.17982364 -0.8329361597 0.1578319644
## 198 Alive 1.355794604 -1.31217975 0.2126240281 -0.5341546811
## 199 Alive 0.342080981 0.71442970 -0.6482593800 -0.2099015734
## 200 Alive -0.390007297 -0.72256040 0.2659366383 -1.3023370226
## 201 Alive -0.278709707 -0.06166132 -0.3047482694 -0.2069801581
## 202 Alive -0.042662340 0.49913934 -0.5186429497 0.4553285736
## 203 Dead -1.773111892 -0.17830822 -1.7400026462 1.2398085147
## 204 Dead 1.250439359 1.30927635 -1.2548155696 0.1212141597
## 205 Alive -1.763032603 -0.39026215 -1.0709293305 0.7285468245
## 206 Alive -1.734908122 0.22532626 -1.3096386361 1.1382811564
## 207 Alive -0.040455138 0.55449852 0.4573444687 -0.4218347821
## 208 Alive -0.686284826 0.13219155 0.6118547014 -0.2432679726
## 209 Alive -0.444359734 -0.28370817 -0.4495876614 -0.0769292704
## 210 Alive 0.691490501 -1.91894081 -0.1931803231 -0.7485897999
## 211 Alive 2.007551495 -1.38730232 -0.5519627527 -0.6174453995
## 212 Dead 2.980951104 0.35496999 -1.5634230702 -0.6219160971
## 213 Alive -0.051043670 1.76211010 1.2088357396 -1.1338711513
## 214 Alive -1.433696923 0.30117834 -1.1167790798 0.7158629306
## 215 Alive 0.663189426 0.17003794 -0.7914480913 0.1781148795
## 216 Dead 2.031410016 -1.22967790 -2.3061777513 2.1455817946
## 217 Dead 0.789603453 -0.46930287 -1.7356512834 -0.3692602528
## 218 Alive 0.673484381 -0.39280224 0.0473568504 1.1650225109
## 219 Alive -1.540903396 -0.09859304 -1.1167612805 0.8029841934
## 220 Dead 4.811125983 2.34468196 -0.3322754239 0.5855998508
## 221 Dead 2.960210184 0.25580109 -1.3532023514 1.1105279220
## 222 Dead 0.548555090 1.20673516 -0.5847280068 1.2403006951
## 223 Alive -1.203818787 0.41491335 0.6516018979 -1.7888960008
## 224 Alive -0.095903547 -0.65584776 -0.5358363119 -1.2541542670
## 225 Alive -1.447284264 -1.00724102 -0.6082703522 -1.5298781643
## 226 Alive -0.721456172 1.13787970 0.8467912909 -2.0802276689
## 227 Alive 2.040310983 0.43242568 -0.2461052925 0.7423873284
## 228 Alive 1.855207556 1.67633604 0.5148301396 -0.1260125667
## 229 Alive -1.362709085 0.28203522 -1.2055884775 0.5729921576
## 230 Alive -0.288896751 0.20730044 0.2845176632 0.6308919312
## 231 Alive -0.418601999 0.23532480 0.2238988269 -0.5027334058
## 232 Alive -1.163850583 0.68497750 -0.8821849871 0.8863377110
## 233 Alive 0.411132602 1.16486925 -0.3493614654 1.3942763398
## 234 Alive -1.693135796 -0.47771445 -1.0852001549 0.2466849979
## 235 Alive -1.469262447 0.58168692 0.2179103849 0.0730339108
## 236 Alive -1.241804213 1.79930936 0.0417415503 0.6900290082
## 237 Alive 3.689808324 1.67054618 0.2271980354 -0.1712036874
## 238 Alive 0.637785394 -1.18641596 0.3164064662 0.3364686684
## 239 Dead 6.741912903 1.29247340 -0.5420542885 0.4573219426
## 240 Alive -1.238593026 -0.23776840 -0.5949271348 -1.3969869040
## 241 Dead 0.823175506 1.06316740 -0.5254541417 -0.6645444043
## 242 Alive 0.046147404 1.10794300 0.9541899343 -1.0517974932
## 243 Alive -0.926653518 -0.47703938 0.3584883210 0.7483755808
## 244 Alive 1.642861658 0.76706108 0.4101327315 -1.6601340760
## 245 Alive 0.577872627 -0.27228218 0.0857683853 -1.3777634787
## 246 Alive -1.754825326 0.80791517 0.5577871077 -0.0676093662
## 247 Alive -2.038325012 0.13688760 -0.0003412363 0.3430358578
## 248 Dead 0.534102452 0.42078510 -1.1547081981 -0.6235503927
## 249 Alive -0.778602587 0.16187841 -0.3007337578 -2.1397103069
## 250 Alive -1.358620602 -0.11871598 -0.0786250759 -1.0668656351
## 251 Alive 0.552972231 -1.32892174 0.2653874378 -1.7448134449
## 252 Alive 0.160512695 -1.07401603 -1.3645629081 0.1229912862
## 253 Alive -0.255760964 -1.55052571 -0.6215940219 -1.4389507212
## 254 Alive 2.380048532 -1.22313608 -0.4828668231 -1.7734074221
## 255 Alive 2.562080786 -0.62564376 -0.7980444051 1.7530531164
## 256 Alive -0.556325503 0.61870762 0.4208116759 0.5833612102
## 257 Alive -1.361977024 0.48557037 -0.3780687286 -0.2263198361
## 258 Alive -1.604168388 0.15729081 -1.1427967214 0.6878894786
## 259 Alive 0.453544197 -0.10135935 -0.0830135546 -1.4480142567
## 260 Alive -0.245088734 -0.21116664 -0.8071754259 0.2429511311
## 261 Alive -0.586494355 0.59713665 -2.4100725243 -0.5973150226
## 262 Alive -0.595783004 -0.97017702 0.1712856607 -1.4091442191
## 263 Alive -0.098509308 -0.71157736 -0.6190102919 -0.8101660640
## 264 Dead -1.732739711 -0.01171917 -0.9714345094 0.9911466978
## 265 Alive -1.312518153 2.21664937 1.0466799279 0.0855880150
## 266 Alive -1.117483636 -1.07344208 -0.1309504223 0.5351107892
## 267 Alive -0.802242010 2.43916871 -0.0658918448 0.5326247945
## 268 Alive 1.779574174 -2.20525734 -1.2254437217 -1.4601618621
## 269 Dead -0.692885384 -0.50625416 -1.6109602188 1.2266062367
## 270 Alive -0.296827034 2.09903244 -0.5356781950 1.0212095064
## 271 Dead 2.648459041 -0.60314173 -1.1623236353 -1.1868983731
## 272 Alive -0.009329958 0.66837011 -0.6089249244 -0.0124265699
## 273 Alive 0.636626889 0.36453000 -1.0956031271 -0.4201642118
## 274 Alive -0.730329225 0.63180054 -0.2775908413 0.0076169716
## 275 Alive 0.329127497 -0.70211196 -1.1270499206 -1.3794822582
## 276 Alive -1.859016837 -0.41444458 -1.0884680056 0.0004891493
## 277 Alive 2.011187895 -1.86028031 -1.4701740451 1.9592818340
## 278 Dead 4.387657320 1.01990704 -1.0694317529 1.0313056985
## 279 Alive -1.562200265 0.50506920 0.3257902808 0.4071536855
## 280 Alive 1.140064695 -0.84165314 0.0475366423 0.1828157194
## 281 Alive -1.592089421 0.68980851 0.0241838972 -0.0763303675
## 282 Alive -0.863852065 0.20642081 -0.8983962803 -1.0667886017
## 283 Dead 1.027169030 1.16456255 -1.0404846287 -0.0396471898
## 284 Alive -0.436517354 -0.42713213 0.0134409058 -0.8973018413
## 285 Alive 0.337411799 -0.24417082 -0.6480989722 -0.0855047074
## 286 Dead 0.922063650 -0.22614793 -1.9443047687 0.7895315305
## 287 Alive 0.074518204 0.02674638 -1.0857966267 0.5553685803
## 288 Alive 0.517903752 0.07720678 0.7802091323 -0.3889323964
## 289 Alive 1.205633993 4.05992941 1.7774871852 0.5243784073
## 290 Dead 5.667322803 1.41683162 0.5192606886 -0.5242010735
## 291 Alive 0.117634314 2.05280704 1.1202906141 -0.2225732744
## 292 Alive -1.257776898 0.99085451 -0.6432249171 0.7239870280
## 293 Dead -1.442594978 0.64860803 -1.1825132672 1.3464166771
## 294 Alive 0.581815447 0.15948370 0.5111637426 -1.5852378542
## 295 Alive 3.192976367 -0.80514579 0.6934590185 -0.6145019682
## 296 Alive -1.664428065 0.44940153 -0.8138817842 0.9169350091
## 297 Alive -1.381280799 -1.04718836 -0.8104653996 -1.2130194950
## 298 Alive -0.359580844 -0.02707621 -0.2139147820 0.7519546558
## 299 Alive -1.295214100 0.90633579 0.3446284016 -0.9705650257
## 300 Alive 1.275367360 -0.46955884 -0.9321790556 1.6880185073
## 301 Alive 0.510190648 -0.47545309 0.1659852525 -1.4398287570
## 302 Alive 0.497692443 0.73632621 -0.7320867366 -0.6396358886
## 303 Alive -0.360524908 1.94049135 -0.0814679929 -1.0578009624
## 304 Alive 0.680162177 4.39853961 1.3939873156 -0.0903894719
## 305 Alive 0.651993920 1.46566547 -0.5054646735 1.4206026417
## 306 Dead 3.788964776 -1.08829199 -1.2835697130 1.5189289232
## 307 Alive 0.324102302 0.44636919 -0.0358560470 -1.7147746806
## 308 Alive 1.241627938 -0.80113200 -0.9370602561 0.5736384332
## 309 Alive -0.511968929 -1.17458566 -0.6546640582 -0.3823368294
## 310 Alive 0.718039754 0.17733890 -0.6884966946 -1.2988653722
## 311 Alive -0.310163020 -1.06311682 -0.8411613032 -0.3440185709
## 312 Alive -1.033055205 1.28803157 -0.7885399882 1.0583019502
## 313 Alive -0.764852259 0.84975776 -0.4166580478 -0.3570104900
## 314 Dead 2.840965510 1.27703956 1.2737033558 -0.0712572107
## 315 Alive -1.178758036 -0.07789715 -0.1547232721 -1.1892312531
## 316 Alive -0.802177079 -0.95036649 -0.6926590212 0.0641135168
## 317 Alive 1.938258838 -1.28408318 -0.7550485265 -0.2456973992
## 318 Alive -1.084340607 0.56509571 -0.3641566428 -0.4657496728
## 319 Alive 5.007927517 1.33213703 0.4628978606 -0.6412930066
## 320 Alive -0.352175349 0.05184295 -1.0595996323 1.1419351290
## 321 Alive -1.645893870 0.67772347 0.5678664419 -0.6516041624
## 322 Alive -0.723629619 0.28418574 -0.9155428645 -1.7398043966
## 323 Alive 2.150497872 -1.85335253 -0.9536747162 -0.9930159522
## 324 Alive 0.219479185 0.70653560 0.4625353948 0.0635989317
## 325 Alive -0.347437994 0.13601327 -0.3616040070 0.0995137840
## 326 Alive -0.234908136 0.38370796 0.3810829977 0.2955102824
## 327 Alive 0.016559745 -0.24813137 0.3418529439 -0.6289931873
## 328 Alive -1.467247701 -0.93657939 -1.0073778050 -1.3484920808
## 329 Alive 1.154836707 -1.65839860 -0.1796696786 0.5786916927
## 330 Alive 0.020892606 0.14389944 0.1408600742 0.1842691926
## 331 Alive 0.169022729 0.24173475 0.6782816134 -1.3801420819
## 332 Dead 0.596241854 0.70051500 -1.8052088015 -0.0053918173
## 333 Alive -1.658882001 -0.32657130 0.2318064743 -0.3636469103
## 334 Alive -1.130296134 0.92484749 -0.3380519552 -0.3013039197
## 335 Alive -0.114349001 -0.27920208 -0.6403335111 -0.2074405468
## 336 Alive -1.180178802 0.03183833 -0.3500656477 -1.0972084429
## 337 Alive 1.016962553 -1.84125842 -1.0359966156 0.1725787385
## 338 Alive 1.874901202 -1.13532877 -0.6093993174 1.0930613053
## 339 Alive -1.674481841 0.44986836 2.1646104925 0.9678148811
## 340 Alive 0.347838749 -0.88857174 0.8771393702 -0.0399280185
## 341 Alive -0.523787799 -0.92658682 1.5418929659 0.1325485002
## 342 Alive -1.191298001 1.23405600 1.7890495622 1.3692564275
## 343 Alive 1.808772263 -1.69685692 0.8907964331 -0.2029722962
## 344 Alive -1.770065768 -0.81617964 1.3539885104 -0.2766980579
## 345 Alive -0.206433118 0.56197089 1.8053747930 1.3814075643
## 346 Alive 0.781356058 -0.26730308 1.4981375832 0.8043655618
## 347 Alive -1.821829245 -1.41978625 1.5929954355 -0.6929508188
## 348 Alive -0.284787326 -0.98055909 2.0711730642 -0.3625595662
## 349 Alive -0.436832085 1.81979653 1.9654352950 0.0409412675
## 350 Alive -1.217940564 -0.03242505 1.5341269350 0.0689673368
## 351 Alive 1.408443279 -0.92755403 2.5527909101 -0.6932672647
## 352 Alive 0.076806137 -0.36230781 1.0569801425 0.7081503355
## 353 Alive -1.371613972 -0.73826316 -0.0390647200 0.5827617423
## 354 Alive -1.864312777 -1.17836386 1.6190160585 -0.8239266507
## 355 Alive -1.989259900 -1.78295952 1.5112558257 -0.6883823148
## 356 Alive -0.666931670 0.04442279 0.9603229118 1.9679277491
## 357 Alive -0.752021652 0.57932223 1.1919215542 0.0297044937
## 358 Dead -0.799705965 -1.07103612 0.3748144882 2.1390626788
## 359 Alive -1.601727166 -1.41026284 0.7915067164 -0.2584759327
## 360 Alive -1.657122757 0.50517962 1.7207936026 1.3778309508
## 361 Alive -0.384493964 -0.88081329 0.5179378168 0.9525680456
## 362 Alive -1.117824446 0.07013439 2.3329630062 -0.8981794794
## 363 Dead 2.156938592 -0.59054334 0.9679981313 1.4564801625
## 364 Dead -0.789754021 -2.12761614 1.4729430325 0.0219314842
## 365 Alive -1.380570918 -1.02926654 1.9974600705 -1.3875631548
## 366 Alive -1.291560292 0.38334086 1.4160677141 1.5258026469
## 367 Alive -0.935262338 0.56231264 2.1242791830 0.3720182728
## 368 Alive 2.492171120 -0.48928746 2.4676282836 1.9668068431
## 369 Alive -0.327363502 -0.84626614 2.2688783371 0.9603180211
## 370 Dead -1.468296601 0.18028669 1.6652393313 1.5773153771
## 371 Alive 0.644477407 1.35334644 2.6883609615 0.5712489712
## 372 Dead 4.369563022 -1.66481832 1.6865361527 0.4901972904
## 373 Alive -2.357052820 -1.26900605 1.5231357317 1.0301102498
## 374 Alive 0.718708019 0.22127710 1.0354060443 0.2583339391
## 375 Alive 1.391878059 0.98004221 1.7111474295 -0.7952838709
## 376 Alive 0.905097897 -0.22694710 2.1140189340 0.5476029310
## 377 Alive 3.157230391 -1.19754195 1.1484347290 1.0599855046
## 378 Alive 0.003135705 -0.90598915 1.6393299343 -1.1011824448
## 379 Alive -0.242056357 -0.73255189 1.7021620290 -0.1866470103
## PC5 PC6 PC7
## 1 -0.332307184 0.814428206 -0.107883916
## 2 0.110810520 -0.048912344 -0.099604504
## 3 -1.007021612 -0.086507916 -0.138527863
## 4 -0.534587533 -0.822748232 0.360506834
## 5 0.527096385 -0.108812986 0.078970882
## 6 -0.430923510 0.183797925 0.433343571
## 7 0.647838054 0.008911379 -0.004657966
## 8 1.901144959 0.543125568 -0.332707934
## 9 -0.346406933 -0.752701863 0.056474342
## 10 -2.024615276 -0.441826427 -1.924448799
## 11 -0.421546565 -0.244944687 0.159851097
## 12 -0.998148360 0.206259597 -0.169273224
## 13 -0.430771477 0.163519054 -0.103667561
## 14 1.267459198 0.132474346 0.108653816
## 15 -0.309831792 -1.324055932 -0.183915616
## 16 0.235344753 0.714919089 0.304537991
## 17 -1.466753080 -0.647376538 0.365592105
## 18 0.363615703 1.097596271 -0.377715183
## 19 -1.122742523 0.334391075 -0.234827285
## 20 -0.848560671 0.808587321 -0.200036177
## 21 -0.381745196 0.322170368 -0.166529357
## 22 0.105717976 0.107803508 0.012805983
## 23 -0.572677371 -0.332323319 -0.202474142
## 24 -1.510109489 0.995998868 0.201016672
## 25 -0.807050880 -2.363493528 0.266625584
## 26 -0.466990302 -0.813907073 -0.571488560
## 27 -0.702827024 -2.160783056 0.281527887
## 28 0.009704223 0.098479393 0.336756957
## 29 -0.228150297 0.004273460 -0.381406184
## 30 -1.283048492 -0.044211599 -0.418300721
## 31 0.475434709 -0.128464996 0.054899611
## 32 0.691915088 -0.357344175 0.183909490
## 33 -0.754412318 -0.597244606 0.289672968
## 34 -0.049714847 0.259235600 0.349194654
## 35 1.283108823 -0.236888897 -0.371166651
## 36 1.416899251 -0.249251785 0.050335461
## 37 2.080438807 0.607590347 -0.462113845
## 38 0.606045480 -0.026797156 0.355817879
## 39 0.948153836 0.166045669 -0.073826942
## 40 0.304358552 -0.162738506 -0.392300116
## 41 1.462378918 -0.522507663 -0.121724380
## 42 1.234755769 0.067225848 0.209115377
## 43 0.342914980 -0.417780877 -0.474060203
## 44 0.834734733 -0.173878940 -0.457967209
## 45 1.653782254 -0.050403121 -0.134114068
## 46 -0.346353752 -0.089979747 -0.491479393
## 47 2.883679498 0.480573605 -0.072323181
## 48 1.372131721 0.228887831 0.155522234
## 49 0.900265041 -0.489991807 -0.227097997
## 50 0.515650798 -0.606582969 -0.101166456
## 51 1.854988517 0.577660866 -0.455756839
## 52 -0.039137939 0.585446120 -0.388137976
## 53 -0.406467811 0.734811073 1.561539615
## 54 0.106389455 1.381511548 0.252947237
## 55 1.220327765 0.358959045 -0.182311216
## 56 1.304773967 0.207910788 0.078632864
## 57 -1.311783436 0.607774154 -0.281869942
## 58 -1.034356670 2.443161543 0.443513680
## 59 0.092369673 0.206843192 0.253038172
## 60 -0.219974275 0.135499206 0.164773439
## 61 -0.418037102 0.648725932 0.351461678
## 62 0.736595283 0.166486526 0.246682271
## 63 0.044579623 -0.513948300 -0.286040883
## 64 -1.251280484 1.163578265 0.263125274
## 65 -0.255173442 -0.009862807 0.134046265
## 66 -0.620332594 -0.730377136 0.337181681
## 67 1.345935978 -1.487448857 -0.149925371
## 68 0.217431325 0.220853759 0.272493773
## 69 -0.390248550 -0.588054260 0.260689981
## 70 -0.266397542 -0.385273067 0.319508713
## 71 -1.764262412 -0.175254751 1.897246402
## 72 1.175874251 -1.300330063 -0.404208363
## 73 1.187096201 0.816322549 -0.225387244
## 74 -1.315635893 -0.060212427 0.165026305
## 75 -1.037240682 -1.649589162 -0.529795744
## 76 -1.564340163 0.569158827 -0.263377372
## 77 0.358667424 -0.165692949 -0.401192949
## 78 0.490508151 0.043436354 0.440699177
## 79 0.788844783 0.327782857 0.371732847
## 80 1.230687259 0.016945132 0.140928440
## 81 0.427134177 -0.877693420 -0.271276638
## 82 0.957971947 0.050656761 0.314869348
## 83 0.543187444 0.024270266 -0.489647178
## 84 1.941501550 -0.428408376 0.144447332
## 85 1.691751149 0.302353058 0.176709283
## 86 1.547734256 -0.930367776 -0.038966156
## 87 0.332021211 0.206974359 1.518547012
## 88 0.214693076 0.773220076 0.387655208
## 89 0.653638646 -0.057425863 0.311702214
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## 259 -0.154195510 0.927279628 0.136024542
## 260 -0.279436645 0.347645497 -0.209884830
## 261 2.411185160 0.229700925 -0.104543344
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## 263 -0.107118411 -0.057284357 -0.187261115
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## 268 0.480018703 -0.067622566 -0.072725103
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## 270 0.236744458 -0.666813685 0.155867363
## 271 1.137440016 -0.136040334 -0.327359471
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## 288 -1.326401252 -1.421668738 0.046595855
## 289 -0.779237256 -2.984199195 0.075859453
## 290 0.057913957 1.319916883 2.001667923
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## 293 -0.103965971 0.021688217 0.270137554
## 294 -0.514462082 -0.049144987 -0.046060227
## 295 -1.279398203 -1.011855498 -0.955345258
## 296 -0.409961580 -0.175912153 0.163389864
## 297 0.131190811 -0.811118093 0.416648260
## 298 -1.081305483 -0.340865035 -0.224224889
## 299 -0.587847432 0.466059600 0.157785884
## 300 -0.857351331 0.558304051 -0.192471657
## 301 -0.586650046 0.750653613 0.459663166
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## 304 -0.359689359 0.426300512 0.141513828
## 305 -0.393377040 0.810547774 0.065859782
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## 309 -0.528559592 -0.335948519 -0.163889426
## 310 0.666658316 0.695110312 -0.089730044
## 311 -0.239649145 -0.421019920 -0.164631917
## 312 -0.014148637 -0.328893323 0.125575320
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## 314 -1.299150219 -0.800239413 -0.264240505
## 315 -0.258297637 -0.079057717 0.438769076
## 316 -0.653215774 -0.386407008 -0.406110560
## 317 -0.386044302 1.041640267 0.390303651
## 318 -0.069947785 -0.189857024 0.234508553
## 319 0.335503981 -1.090183460 0.762300322
## 320 -0.354514092 0.386282802 -0.239807387
## 321 -1.130232840 0.134404520 0.127105246
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## 325 -0.602584780 0.533845103 -0.328861238
## 326 -1.313248723 -0.465612342 -0.352871158
## 327 -1.073354029 -0.163023346 0.003333250
## 328 0.464904725 -0.798713796 0.164392019
## 329 -1.773817068 0.481838526 -1.448359073
## 330 -0.953519579 -1.226111979 -0.366016068
## 331 -0.971815989 1.020308661 0.044230674
## 332 1.465700551 1.056394345 -0.394589336
## 333 -1.209182254 -1.007313550 0.374213944
## 334 -0.112208131 0.492601789 0.244276984
## 335 -0.257747260 0.411613111 -0.135788109
## 336 -0.005358715 -0.280767946 0.263720304
## 337 -0.567197423 0.160862506 -0.192753984
## 338 -1.160229327 0.791036742 0.678047807
## 339 0.135461099 0.126529280 0.120748763
## 340 1.772672225 0.262317102 -0.088849352
## 341 0.785980424 0.041119374 -0.483927739
## 342 0.892653715 -0.678266870 -0.258446039
## 343 1.489618576 1.445310485 0.036985630
## 344 1.166492368 -0.175915279 0.027902348
## 345 0.495893161 0.564004554 -0.503273137
## 346 1.134248369 -1.123890798 -0.049820336
## 347 0.865846962 -0.529962184 0.213624141
## 348 0.392274537 0.448319463 -0.109057231
## 349 1.657960929 0.164185074 -0.178027089
## 350 1.157904466 0.343302649 0.295711308
## 351 0.150225917 1.064600476 -0.399557062
## 352 1.356282603 0.402428026 -0.264910522
## 353 2.417181597 -0.039235833 0.080955691
## 354 0.990897877 -0.401278508 0.033682397
## 355 0.805384073 -0.845062983 0.190359077
## 356 0.821582895 0.916027349 -0.545821754
## 357 1.852331941 0.946629462 0.303161216
## 358 1.010092176 -0.119192699 -0.421977595
## 359 1.601877583 -0.474603729 0.232244290
## 360 0.405279647 0.620269650 0.217072532
## 361 1.560400572 0.290272477 -0.446292100
## 362 0.738754653 0.807055770 0.427223893
## 363 1.063503699 1.725250067 0.275888197
## 364 0.410727684 -0.573212533 -0.177662617
## 365 0.968366183 -0.242829260 0.310782840
## 366 0.762317564 -0.025556816 0.310309937
## 367 0.718006182 -0.369535370 0.246732337
## 368 -0.727490529 0.794924538 0.929445109
## 369 -0.407816836 -0.044906053 0.144701045
## 370 0.412661443 -0.730353345 0.202922032
## 371 0.440528158 0.105639703 -0.429239913
## 372 0.760040778 -0.245135971 0.186120856
## 373 0.074632682 -0.823120736 0.174853047
## 374 1.891779073 1.126518713 -0.084801083
## 375 2.265775349 -0.200011773 -0.549385252
## 376 0.603860387 -1.229143214 0.135743929
## 377 1.186962665 -0.299503313 0.743333133
## 378 1.359035590 0.410392839 -0.361555114
## 379 0.800865246 0.837670932 -0.196874004
# Means of scores for all the PC's classified by Survival status
tabmeansPC <- aggregate(sparrtyp_pca[,2:6],by=list(Survivor=Cancer$Survivor),mean)
tabmeansPC
## Survivor PC1 PC2 PC3 PC4 PC5
## 1 Alive -0.191643 -0.04773213 0.1087994 -0.08377152 -0.1049705
## 2 Dead 1.039420 0.25888613 -0.5900986 0.45435399 0.5693316
## Inference
## PC1, the mean value for the Alive group is negative (-0.191643), while for the Dead group, it is positive (1.039420), indicating that PC1 has a strong influence on separating the two groups. Similarly, for PC2 and PC5, the mean values for the Dead group are higher than those for the Alive group, indicating that these components also contribute to the separation of the two groups.
## For PC3 and PC4, the mean values are positive for the Alive group and negative for the Dead group. This suggests that these components are less important in distinguishing between the two groups of cancer patients.
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Survivor)),]
tabmeansPC
## Survivor PC1 PC2 PC3 PC4 PC5
## 2 Dead 1.039420 0.25888613 -0.5900986 0.45435399 0.5693316
## 1 Alive -0.191643 -0.04773213 0.1087994 -0.08377152 -0.1049705
## From the tabmeansPC we can infer that the patients who died have higher average values of PC1 to PC5 compared to those who survived.
tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
## 2 1
## PC1 1.0394196 -0.19164299
## PC2 0.2588861 -0.04773213
## PC3 -0.5900986 0.10879943
## PC4 0.4543540 -0.08377152
## PC5 0.5693316 -0.10497052
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Survivor))
tabfmeans
## Dead Alive
## PC1 1.0394196 -0.19164299
## PC2 0.2588861 -0.04773213
## PC3 -0.5900986 0.10879943
## PC4 0.4543540 -0.08377152
## PC5 0.5693316 -0.10497052
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(sparrtyp_pca[,2:6],by=list(Survivor=Cancer$Survivor),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Survivor))
tabfsds
## Alive Dead
## PC1 1.3045077 1.9921081
## PC2 1.0622596 1.1781697
## PC3 0.9845002 1.0805810
## PC4 0.9561011 0.9236866
## PC5 0.9104233 0.8906488
t.test(PC1~Cancer$Survivor,data=sparrtyp_pca)
##
## Welch Two Sample t-test
##
## data: PC1 by Cancer$Survivor
## t = -4.5695, df = 67.457, p-value = 2.14e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
## -1.7687358 -0.6933893
## sample estimates:
## mean in group Alive mean in group Dead
## -0.191643 1.039420
## The t-test is used to determine whether there is a significant difference between the mean PC1 scores of the "Alive" and "Dead" groups.
## The output shows that the t-statistic is -4.5695 and the p-value is 2.14e-05, which is much less than 0.05, the commonly used significance level. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the mean PC1 scores of the "Alive" and "Dead" groups.
t.test(PC2~Cancer$Survivor,data=sparrtyp_pca)
##
## Welch Two Sample t-test
##
## data: PC2 by Cancer$Survivor
## t = -1.8642, df = 76.377, p-value = 0.06614
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
## -0.63417884 0.02094233
## sample estimates:
## mean in group Alive mean in group Dead
## -0.04773213 0.25888613
## For PC2, the p-value of the t-test is greater than 0.05, indicating that there is no strong evidence to suggest that the mean values of PC2 are different between the two groups.
t.test(PC3~Cancer$Survivor,data=sparrtyp_pca)
##
## Welch Two Sample t-test
##
## data: PC3 by Cancer$Survivor
## t = 4.6266, df = 76.785, p-value = 1.482e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
## 0.3980823 0.9997138
## sample estimates:
## mean in group Alive mean in group Dead
## 0.1087994 -0.5900986
## The p-values for the t-tests of PC1, PC2, and PC3 between the two groups (Alive and Dead) are 2.14e-05, 0.06614, and 1.482e-05, respectively. These p-values indicate that there is strong evidence to reject the null hypothesis of no difference in the mean values of the principal components between the two groups for PC1 and PC3.
## However, for PC2, the p-value is relatively high (0.06614), which suggests that there is no strong evidence to reject the null hypothesis of no difference in the mean values of PC2 between the two groups.
t.test(PC4~Cancer$Survivor,data=sparrtyp_pca)
##
## Welch Two Sample t-test
##
## data: PC4 by Cancer$Survivor
## t = -4.0892, df = 82.592, p-value = 9.998e-05
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
## -0.7998846 -0.2763664
## sample estimates:
## mean in group Alive mean in group Dead
## -0.08377152 0.45435399
## Based on the t-tests, we can see that there are significant differences in the means of PC1, PC3, and PC4 between the Alive and Dead groups, as evidenced by their low p-values (p < 0.05). However, there is no significant difference in the means of PC2 between the two groups (p > 0.05).
t.test(PC5~Cancer$Survivor,data=sparrtyp_pca)
##
## Welch Two Sample t-test
##
## data: PC5 by Cancer$Survivor
## t = -5.325, df = 81.947, p-value = 8.655e-07
## alternative hypothesis: true difference in means between group Alive and group Dead is not equal to 0
## 95 percent confidence interval:
## -0.9262125 -0.4223918
## sample estimates:
## mean in group Alive mean in group Dead
## -0.1049705 0.5693316
## F ratio tests
var.test(PC1~Cancer$Survivor,data=sparrtyp_pca)
##
## F test to compare two variances
##
## data: PC1 by Cancer$Survivor
## F = 0.42881, num df = 319, denom df = 58, p-value = 3.503e-06
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.2799208 0.6214510
## sample estimates:
## ratio of variances
## 0.4288125
var.test(PC2~Cancer$Survivor,data=sparrtyp_pca)
##
## F test to compare two variances
##
## data: PC2 by Cancer$Survivor
## F = 0.81292, num df = 319, denom df = 58, p-value = 0.2734
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.5306564 1.1781079
## sample estimates:
## ratio of variances
## 0.8129159
var.test(PC3~Cancer$Survivor,data=sparrtyp_pca)
##
## F test to compare two variances
##
## data: PC3 by Cancer$Survivor
## F = 0.83007, num df = 319, denom df = 58, p-value = 0.3235
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.5418571 1.2029746
## sample estimates:
## ratio of variances
## 0.8300744
var.test(PC4~Cancer$Survivor,data=sparrtyp_pca)
##
## F test to compare two variances
##
## data: PC4 by Cancer$Survivor
## F = 1.0714, num df = 319, denom df = 58, p-value = 0.7705
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.6994008 1.5527366
## sample estimates:
## ratio of variances
## 1.071417
var.test(PC5~Cancer$Survivor,data=sparrtyp_pca)
##
## F test to compare two variances
##
## data: PC5 by Cancer$Survivor
## F = 1.0449, num df = 319, denom df = 58, p-value = 0.8655
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.6820898 1.5143045
## sample estimates:
## ratio of variances
## 1.044898
# Levene's tests (one-sided)
library(car)
## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:purrr':
##
## some
##
## The following object is masked from 'package:dplyr':
##
## recode
(LTPC1 <- leveneTest(PC1~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 13.637 0.0002545 ***
## 377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 0.0001272506
(LTPC2 <- leveneTest(PC2~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 2.0564 0.1524
## 377
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.0761985
(LTPC3 <- leveneTest(PC3~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.1773 0.6739
## 377
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 0.3369607
(LTPC4 <- leveneTest(PC4~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.1316 0.717
## 377
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 0.358511
(LTPC5 <- leveneTest(PC5~Cancer$Survivor,data=sparrtyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.0035 0.953
## 377
(p_PC5_1sided <- LTPC5[[3]][1]/2)
## [1] 0.4765143
# Plotting the scores for the first and second components
plot(eigen_Cancer, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree Diagram")
plot(log(eigen_Cancer), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")
print(summary(Cancer_pca))
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion 0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
diag(cov(Cancer_pca$x))
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## 2.2447716 1.1776466 1.0614934 0.9405242 0.8811341 0.5071959 0.1872342
xlim <- range(Cancer_pca$x[,1])
Cancer_pca$x[,1]
## [1] -1.441559363 0.466697152 1.724644704 -1.727412749 0.084534880
## [6] -0.987174108 -1.289312885 0.457476281 5.013544810 1.966110970
## [11] -1.709742154 1.323214712 -0.047344848 -0.023379894 1.042993427
## [16] -0.954171084 -0.510183493 0.248390384 -0.386424810 -0.212235416
## [21] 0.001291199 0.547237523 -0.581794885 1.484574719 0.730385134
## [26] 1.384044724 2.503197607 -1.094732396 -0.040233637 -0.913495245
## [31] 0.044817272 -1.310023914 -1.750326793 -0.860691537 1.293140200
## [36] -1.575412171 0.505620687 -1.445729993 -0.240634131 -0.335231355
## [41] 2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
## [46] 0.653344872 -0.903132282 -1.570956435 0.407142180 -2.095133885
## [51] 0.145196356 0.438754344 2.005777230 1.526981600 -1.762004433
## [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
## [61] -0.899762531 -1.006446958 -0.437812701 1.712300783 -1.263885916
## [66] -1.604219653 4.488026052 -0.665172931 -1.668377900 -1.130422629
## [71] 3.316812797 2.172380940 0.572326326 -1.827615023 0.720276568
## [76] 0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
## [81] 0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
## [86] 0.909892498 2.680823986 1.353531002 -1.678967186 -2.304099591
## [91] 0.741204117 -0.809147683 -0.790428226 1.549314451 -1.647991336
## [96] -0.268121798 -0.103534223 -0.776307350 1.103113756 -0.409442426
## [101] 4.633190126 -0.740349810 0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410 0.345220609 -1.364096376 -0.387521866 0.491580932
## [111] -1.087373932 1.210180885 1.869006469 0.492734252 0.889433533
## [116] -0.849321798 1.382626614 -0.876114257 0.129510618 0.006142764
## [121] -0.669636518 1.757579745 1.875711497 0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005 0.585398503 -1.786207788 -1.427017695 0.756062138
## [136] 0.145449916 -0.274324587 -0.438129117 1.064299809 2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125 0.505611656 0.247551976
## [146] -0.602802743 -1.272341157 2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156] 2.182293451 -0.839030427 -1.567211240 -0.656681669 1.746317858
## [161] 0.576848393 -1.591129974 -1.734769097 -1.257058960 0.171012852
## [166] 0.763873736 -0.648233872 4.075761272 0.108096807 -1.498040609
## [171] 0.047885996 1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176] 1.309706033 -0.190859319 -1.150520519 1.562083350 0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409 1.401099127 3.044609211
## [186] -0.608848019 0.869481448 -0.300778748 0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346 3.146400023
## [196] -1.646968799 0.194381857 1.355794604 0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892 1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734 0.691490501
## [211] 2.007551495 2.980951104 -0.051043670 -1.433696923 0.663189426
## [216] 2.031410016 0.789603453 0.673484381 -1.540903396 4.811125983
## [221] 2.960210184 0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172 2.040310983 1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583 0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213 3.689808324 0.637785394 6.741912903 -1.238593026
## [241] 0.823175506 0.046147404 -0.926653518 1.642861658 0.577872627
## [246] -1.754825326 -2.038325012 0.534102452 -0.778602587 -1.358620602
## [251] 0.552972231 0.160512695 -0.255760964 2.380048532 2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388 0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010 1.779574174 -0.692885384 -0.296827034
## [271] 2.648459041 -0.009329958 0.636626889 -0.730329225 0.329127497
## [276] -1.859016837 2.011187895 4.387657320 -1.562200265 1.140064695
## [281] -1.592089421 -0.863852065 1.027169030 -0.436517354 0.337411799
## [286] 0.922063650 0.074518204 0.517903752 1.205633993 5.667322803
## [291] 0.117634314 -1.257776898 -1.442594978 0.581815447 3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100 1.275367360
## [301] 0.510190648 0.497692443 -0.360524908 0.680162177 0.651993920
## [306] 3.788964776 0.324102302 1.241627938 -0.511968929 0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259 2.840965510 -1.178758036
## [316] -0.802177079 1.938258838 -1.084340607 5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619 2.150497872 0.219479185 -0.347437994
## [326] -0.234908136 0.016559745 -1.467247701 1.154836707 0.020892606
## [331] 0.169022729 0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802 1.016962553 1.874901202 -1.674481841 0.347838749
## [341] -0.523787799 -1.191298001 1.808772263 -1.770065768 -0.206433118
## [346] 0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351] 1.408443279 0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446 2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338 2.492171120 -0.327363502 -1.468296601
## [371] 0.644477407 4.369563022 -2.357052820 0.718708019 1.391878059
## [376] 0.905097897 3.157230391 0.003135705 -0.242056357
Cancer_pca$x
## PC1 PC2 PC3 PC4 PC5
## [1,] -1.441559363 1.84595445 -0.3691842456 0.8313546497 -0.332307184
## [2,] 0.466697152 0.06803649 -0.6236808487 -0.3679040103 0.110810520
## [3,] 1.724644704 -0.46933933 -0.1593826887 0.5351088884 -1.007021612
## [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
## [5,] 0.084534880 -1.24252757 -1.5702796993 -0.3040439925 0.527096385
## [6,] -0.987174108 0.58301426 0.1669091720 -0.9999683133 -0.430923510
## [7,] -1.289312885 0.33343114 -1.1225709379 -0.4660831193 0.647838054
## [8,] 0.457476281 -0.43703336 -2.3348237400 -0.5798103154 1.901144959
## [9,] 5.013544810 -0.35127563 0.3138865965 -0.6789485742 -0.346406933
## [10,] 1.966110970 0.57900951 0.8436785098 1.1971488330 -2.024615276
## [11,] -1.709742154 0.39272616 -0.8797546127 1.0395229446 -0.421546565
## [12,] 1.323214712 -1.40692828 0.0010448762 -0.8532983622 -0.998148360
## [13,] -0.047344848 0.20982069 -0.8615166802 1.1288786920 -0.430771477
## [14,] -0.023379894 1.83512622 -0.8543600804 -0.5919635549 1.267459198
## [15,] 1.042993427 1.19479846 -0.1106365956 0.7578922926 -0.309831792
## [16,] -0.954171084 1.25373181 -0.8631921253 0.4922727293 0.235344753
## [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
## [18,] 0.248390384 0.43156365 -0.4623851738 -1.2333483190 0.363615703
## [19,] -0.386424810 -0.37494859 0.5477775527 -1.3442739171 -1.122742523
## [20,] -0.212235416 0.44848661 -0.0814638947 0.1978257208 -0.848560671
## [21,] 0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
## [22,] 0.547237523 0.35323566 -0.8945832960 0.4857434118 0.105717976
## [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
## [24,] 1.484574719 -1.12275223 0.4930197218 -0.8534326311 -1.510109489
## [25,] 0.730385134 3.01009366 1.5328340955 -0.0845516282 -0.807050880
## [26,] 1.384044724 2.86730858 0.7935319092 0.4879719811 -0.466990302
## [27,] 2.503197607 1.86942247 1.6035708576 -1.0898911376 -0.702827024
## [28,] -1.094732396 0.13919430 -0.2430526831 -1.3348711724 0.009704223
## [29,] -0.040233637 0.24894946 -0.5823916977 0.1870202613 -0.228150297
## [30,] -0.913495245 -0.27255918 -0.2249052502 0.7136559763 -1.283048492
## [31,] 0.044817272 -1.24749459 -1.5147400984 -0.3403352312 0.475434709
## [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835 0.691915088
## [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
## [34,] -0.860691537 1.17774354 -0.4731321013 0.2383866081 -0.049714847
## [35,] 1.293140200 1.12837700 -1.0955034983 -0.3513923420 1.283108823
## [36,] -1.575412171 -0.65517742 1.1178980897 -0.0145585733 1.416899251
## [37,] 0.505620687 0.48204717 0.6768751198 0.9826148200 2.080438807
## [38,] -1.445729993 -0.53420180 2.0397881463 -0.4191403509 0.606045480
## [39,] -0.240634131 -1.38008841 1.2981310791 0.0234566336 0.948153836
## [40,] -0.335231355 -0.71567154 2.2622815166 -0.2598837684 0.304358552
## [41,] 2.392046521 -0.75381886 0.6808155988 1.7849935943 1.462378918
## [42,] -1.496209472 -0.05147919 0.8362058172 1.4463882147 1.234755769
## [43,] -1.238156754 -1.73396163 1.0838915624 1.1966166369 0.342914980
## [44,] -0.122858339 -0.41520397 1.7259286489 0.2467343049 0.834734733
## [45,] -1.614959830 -0.21262796 0.8270352673 0.5084458503 1.653782254
## [46,] 0.653344872 -1.45282335 1.6923961454 1.7730389364 -0.346353752
## [47,] -0.903132282 0.00288121 0.2891894480 -0.3828977838 2.883679498
## [48,] -1.570956435 -0.13307164 0.7378711359 1.2691205943 1.372131721
## [49,] 0.407142180 -0.18484286 1.8224576827 0.3406571927 0.900265041
## [50,] -2.095133885 -0.24603762 1.3075254314 1.5865972660 0.515650798
## [51,] 0.145196356 -0.72051716 1.2885099274 -1.1072761596 1.854988517
## [52,] 0.438754344 -1.67207421 0.9831353778 2.3512915236 -0.039137939
## [53,] 2.005777230 -2.95342227 1.2688959631 1.7356814675 -0.406467811
## [54,] 1.526981600 -1.02119752 1.4223445513 1.8001650835 0.106389455
## [55,] -1.762004433 0.13389155 1.3060891880 0.4365138287 1.220327765
## [56,] -1.584099552 -0.27233552 1.1461680461 0.3643457178 1.304773967
## [57,] -0.496130040 0.33490544 0.2711418287 0.1648088615 -1.311783436
## [58,] -0.310631363 3.07311289 1.8743230894 -1.7983452746 -1.034356670
## [59,] -1.133478035 0.41599332 -0.4379284603 -0.8528069490 0.092369673
## [60,] -1.203472671 0.78226143 -0.1914939617 -0.4844823758 -0.219974275
## [61,] -0.899762531 1.31926126 0.1811318594 -0.4938217806 -0.418037102
## [62,] -1.006446958 0.35539993 -1.2221294160 -0.3469217710 0.736595283
## [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576 0.044579623
## [64,] 1.712300783 -0.45593265 -0.1013381728 0.5911078860 -1.251280484
## [65,] -1.263885916 1.17224839 -0.6291534095 0.9206949813 -0.255173442
## [66,] -1.604219653 -0.82712464 0.0494208809 -1.5797529143 -0.620332594
## [67,] 4.488026052 1.14176192 -0.1231038156 -1.5112898673 1.345935978
## [68,] -0.665172931 0.68451038 0.1453995807 -2.0258292592 0.217431325
## [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
## [70,] -1.130422629 0.23695569 -0.1769384999 -0.7612337767 -0.266397542
## [71,] 3.316812797 -1.81535426 0.5502180418 -0.2694003925 -1.764262412
## [72,] 2.172380940 2.85911092 -0.9844345887 1.6403461146 1.175874251
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## [75,] 0.720276568 1.70219107 0.6872975038 0.8005007414 -1.037240682
## [76,] 0.849193077 -1.14260361 0.1217975270 -0.0272015985 -1.564340163
## [77,] -0.640547040 -0.61272303 1.3854969929 1.5959470836 0.358667424
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## [80,] -1.769164273 -0.22777378 0.5215512977 1.9330657865 1.230687259
## [81,] 0.718379560 0.42702578 2.7049430509 0.0009902972 0.427134177
## [82,] -1.678008963 -0.30727716 0.8345249461 1.7090923528 0.957971947
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## [84,] -1.627068924 -1.17405222 0.1883777552 0.6241466387 1.941501550
## [85,] -1.331489281 -0.34160016 0.9121167916 0.1344506975 1.691751149
## [86,] 0.909892498 -0.53731582 1.4060161653 -0.0311065615 1.547734256
## [87,] 2.680823986 -2.87516871 1.2736995009 0.6959415006 0.332021211
## [88,] 1.353531002 -2.37316783 1.3254482077 0.7127875562 0.214693076
## [89,] -1.678967186 -0.70552936 1.6695940259 0.1038284595 0.653638646
## [90,] -2.304099591 -0.48981820 1.6210427235 0.9780934643 0.289061393
## [91,] 0.741204117 -2.34543537 1.4452706433 0.5998522096 0.088681106
## [92,] -0.809147683 -0.48805441 0.7203787577 -1.4686194537 2.727281577
## [93,] -0.790428226 -1.28394744 1.3498973595 1.2856985141 0.289629154
## [94,] 1.549314451 1.05942412 1.1109895492 0.1457696503 2.619577831
## [95,] -1.647991336 -0.27927996 1.6891990873 0.5048525410 0.651509510
## [96,] -0.268121798 -0.13194343 0.7385162603 1.3684964706 1.386087535
## [97,] -0.103534223 -1.33945241 -0.5191543874 1.0167737783 2.587808079
## [98,] -0.776307350 -0.99454099 1.0504553950 1.2109563269 0.697921783
## [99,] 1.103113756 -1.77799849 -1.0931648334 -0.0122323381 -0.394650374
## [100,] -0.409442426 0.35492707 -1.0502000077 1.4204609639 -0.397600387
## [101,] 4.633190126 2.16526818 0.6239105977 -1.1366907435 0.716197325
## [102,] -0.740349810 1.21149156 -0.0348952140 -1.2669488699 0.172769662
## [103,] 0.704221402 -1.11279489 -2.7553374907 -0.4028612238 2.065387989
## [104,] -0.385204834 -0.52764189 -1.2886177272 0.4419425766 0.047208371
## [105,] -0.068793640 0.07508422 -0.6067830446 -0.3162015548 -0.041201539
## [106,] -0.692576410 -0.91636560 -1.3471231484 0.7054513599 -0.195224769
## [107,] 0.345220609 -0.15476507 -1.9375149484 0.6213467649 0.919975929
## [108,] -1.364096376 0.64909093 -0.7204212843 1.0498159217 -0.453733562
## [109,] -0.387521866 -1.16290394 0.1995560232 -2.1751452860 -0.561207544
## [110,] 0.491580932 1.59726077 -0.0288299149 0.6365139827 -0.572820855
## [111,] -1.087373932 0.96622658 -0.4850478973 0.2957151405 -0.135727528
## [112,] 1.210180885 -2.10091879 -0.7122063654 -1.4443151802 -0.137991722
## [113,] 1.869006469 1.83583553 0.7046224722 -1.0701872221 -0.128090086
## [114,] 0.492734252 -0.45633393 -0.5614007104 -0.8951702764 0.019316758
## [115,] 0.889433533 -1.50731469 0.2004002058 -0.2364464439 -1.562982457
## [116,] -0.849321798 0.50645649 -1.0584322308 -0.1780669707 0.591477024
## [117,] 1.382626614 -1.86070361 -0.1224339395 -0.3673855944 -1.331526169
## [118,] -0.876114257 1.31244321 0.5402724456 0.6865577157 -1.229611547
## [119,] 0.129510618 -0.29073195 0.1371234823 -1.0140234437 -0.673787799
## [120,] 0.006142764 0.12672993 -0.8224846986 -0.0976817279 0.094607214
## [121,] -0.669636518 -0.67017693 -0.0910644210 0.8278709329 -1.597334402
## [122,] 1.757579745 -1.15217572 -0.1806146788 -1.0023054945 -0.655282364
## [123,] 1.875711497 0.92049908 -0.1305383937 -0.2267912179 0.248083035
## [124,] 0.312604564 0.73821191 0.3983729256 0.0063600881 -1.061968175
## [125,] -0.681074580 1.46363098 -0.7243706847 -0.3192569625 0.623824012
## [126,] -0.863182056 1.24685123 -1.9912585523 1.1497711812 1.220471619
## [127,] -0.118572831 -0.70053670 0.2417380654 -2.0356708316 -0.481456587
## [128,] -1.423953866 -0.28566927 -1.5423434161 0.5267774639 0.380919478
## [129,] -1.441335172 -0.03524627 -0.5051970790 -0.2755060729 -0.294085119
## [130,] -0.856545337 0.21574546 -0.3501704930 -1.3208020069 0.238694945
## [131,] -1.307398005 0.79423090 -1.0835136941 0.4150931199 0.325144944
## [132,] 0.585398503 -0.41679342 -0.4499848326 -0.4042504411 -0.217308431
## [133,] -1.786207788 -0.17673804 -0.0665424655 -0.3670738391 -0.874193293
## [134,] -1.427017695 -0.63688709 -0.4649731902 -0.8892591027 -0.285329535
## [135,] 0.756062138 -0.13112369 -1.3636990615 0.5752861401 0.501840322
## [136,] 0.145449916 1.69976295 -0.3153802001 -1.9246355296 1.223740806
## [137,] -0.274324587 -0.57433529 -0.2583518619 -1.1336704462 -0.355978066
## [138,] -0.438129117 0.74050108 -0.3404267839 0.7633673055 -0.744750043
## [139,] 1.064299809 0.61136855 -0.6550235320 0.9211144934 -0.100363294
## [140,] 2.098096298 -0.42706015 0.8620866598 -0.4563567888 -1.581028316
## [141,] -1.849943605 -0.47094945 -0.5180573283 -0.5701157634 -0.361247028
## [142,] -0.732556857 -0.13070679 0.3510392562 -2.5238550573 -0.054159239
## [143,] -0.608595125 1.35155467 -0.7057542462 -0.7165766057 0.738930758
## [144,] 0.505611656 1.09999711 -0.8457725436 0.9361832967 0.038535375
## [145,] 0.247551976 0.46673882 -0.7913160371 0.0399880240 0.108618695
## [146,] -0.602802743 -0.23260921 0.5437161698 -0.0788003168 -1.731152433
## [147,] -1.272341157 0.63788399 0.2396679916 -1.6177473606 -0.203905033
## [148,] 2.651497970 -0.83742214 -0.8602918415 -0.9187276925 0.528132953
## [149,] -1.824221268 -0.45358497 -1.0788845841 0.9216453730 -0.461933940
## [150,] -0.352147008 -0.02439510 -0.1582340020 0.1140579142 -0.848242620
## [151,] -1.129437762 0.24550127 0.4252415970 -2.4757263934 -0.148360413
## [152,] -0.549974224 0.36383145 -0.6269521199 1.0856493132 -0.698788478
## [153,] -1.104925141 0.73145555 -0.9068622646 0.3853904201 0.128318661
## [154,] -1.260493668 0.67356911 0.3950426508 -0.1537212632 -1.029294466
## [155,] -1.263788087 0.89343258 -0.8613170835 1.0342322348 -0.179152647
## [156,] 2.182293451 -0.70621431 0.3489551723 1.5351765574 -2.192394663
## [157,] -0.839030427 0.51161725 -1.0551051340 -0.7935641661 0.844991207
## [158,] -1.567211240 -0.76592187 -0.0382695651 -2.2426462201 -0.151819917
## [159,] -0.656681669 -1.17053344 -1.0085651375 -0.1509452878 -0.245449969
## [160,] 1.746317858 1.20029090 -1.6249506696 0.9407644883 1.428460815
## [161,] 0.576848393 1.03248254 -1.8769456788 1.1403757019 1.148244806
## [162,] -1.591129974 -0.30100995 -1.4737482868 -0.1586928611 0.631200467
## [163,] -1.734769097 -0.63230165 -0.6993991424 0.0578306174 -0.522553451
## [164,] -1.257058960 0.98743371 0.2695795040 -0.5173988569 -0.667657584
## [165,] 0.171012852 0.73662045 -0.6335336460 0.6662455703 -0.148260447
## [166,] 0.763873736 -1.48595671 -1.3893183822 1.8933152957 -0.923231546
## [167,] -0.648233872 0.65902369 -0.3523707692 -0.3496173059 0.053036529
## [168,] 4.075761272 -0.02211354 1.3258187920 -1.7139363992 -0.985583605
## [169,] 0.108096807 -0.74362678 -1.3323697664 -0.3209218040 0.450579099
## [170,] -1.498040609 0.19056435 0.2761281170 -0.9725452192 -0.798104332
## [171,] 0.047885996 0.72229011 -0.4345521427 1.3431830404 -0.865118234
## [172,] 1.337596168 -0.99890019 -0.4764831468 1.0952509419 -1.281949522
## [173,] -1.358485537 -0.11022223 -0.3457867052 -1.0397848770 -0.109872739
## [174,] -1.872027381 0.13432597 -0.2581474106 0.2022369490 -0.831155436
## [175,] -1.311243234 1.36865781 0.6373415177 -0.4090917149 -1.011660986
## [176,] 1.309706033 -1.47375458 -0.5852915698 -1.0931889293 -0.278496918
## [177,] -0.190859319 1.67724390 -0.7080844449 0.4280689948 0.590243975
## [178,] -1.150520519 -0.39541176 -0.6403158755 -1.4507416448 0.354044928
## [179,] 1.562083350 2.47954880 0.2323943105 -0.3200123444 0.378480572
## [180,] 0.457663612 -0.14582329 -0.6638729701 0.7733241568 -0.509222553
## [181,] -1.138195339 2.01560621 0.8465374351 -0.4823983801 -0.986316252
## [182,] -0.007740653 0.82444862 -0.0002346095 0.3074323320 -0.807425073
## [183,] -1.442466409 0.10416344 -2.2744315999 1.2646597948 1.004394643
## [184,] 1.401099127 0.69145106 -0.3432001965 -0.4552169029 0.392406398
## [185,] 3.044609211 -0.84163842 0.2359688651 -0.0030339038 -1.095598605
## [186,] -0.608848019 0.10718396 -0.0234540132 0.6904571295 -1.303809693
## [187,] 0.869481448 -1.63077965 -0.5698543214 1.5434401088 -1.685405103
## [188,] -0.300778748 0.05603470 -0.4615545760 0.1636332520 -0.514773465
## [189,] 0.636747830 2.30234603 1.1644239379 0.0093990323 -1.179875943
## [190,] -1.117892469 0.18858115 -0.3253204166 -1.3032488160 0.106289330
## [191,] -0.433517740 -0.06760578 -0.8846842302 0.3292279071 -0.195203996
## [192,] -2.074508151 -0.53753951 -0.4998051808 -0.0243119417 -0.707539233
## [193,] -0.943857160 1.31427799 -0.3177697220 0.3467708448 -0.211477339
## [194,] -0.671437346 -1.01840193 -0.5258171064 -0.3862781611 -0.631526388
## [195,] 3.146400023 -0.15766658 -0.4540461596 -0.5782133325 0.335024707
## [196,] -1.646968799 0.07418381 -1.4456195095 0.8218169329 0.234350644
## [197,] 0.194381857 0.17982364 -0.8329361597 0.1578319644 0.012979177
## [198,] 1.355794604 -1.31217975 0.2126240281 -0.5341546811 -1.308712601
## [199,] 0.342080981 0.71442970 -0.6482593800 -0.2099015734 0.202983167
## [200,] -0.390007297 -0.72256040 0.2659366383 -1.3023370226 -0.917914031
## [201,] -0.278709707 -0.06166132 -0.3047482694 -0.2069801581 -0.550875712
## [202,] -0.042662340 0.49913934 -0.5186429497 0.4553285736 -0.344718375
## [203,] -1.773111892 -0.17830822 -1.7400026462 1.2398085147 0.256196652
## [204,] 1.250439359 1.30927635 -1.2548155696 0.1212141597 1.352914243
## [205,] -1.763032603 -0.39026215 -1.0709293305 0.7285468245 -0.342694606
## [206,] -1.734908122 0.22532626 -1.3096386361 1.1382811564 -0.036594174
## [207,] -0.040455138 0.55449852 0.4573444687 -0.4218347821 -1.104169327
## [208,] -0.686284826 0.13219155 0.6118547014 -0.2432679726 -1.594675721
## [209,] -0.444359734 -0.28370817 -0.4495876614 -0.0769292704 -0.578337456
## [210,] 0.691490501 -1.91894081 -0.1931803231 -0.7485897999 -1.218968830
## [211,] 2.007551495 -1.38730232 -0.5519627527 -0.6174453995 -0.374722131
## [212,] 2.980951104 0.35496999 -1.5634230702 -0.6219160971 1.802482148
## [213,] -0.051043670 1.76211010 1.2088357396 -1.1338711513 -0.589252139
## [214,] -1.433696923 0.30117834 -1.1167790798 0.7158629306 0.010513237
## [215,] 0.663189426 0.17003794 -0.7914480913 0.1781148795 0.204851463
## [216,] 2.031410016 -1.22967790 -2.3061777513 2.1455817946 0.319442130
## [217,] 0.789603453 -0.46930287 -1.7356512834 -0.3692602528 1.111404116
## [218,] 0.673484381 -0.39280224 0.0473568504 1.1650225109 -1.817685120
## [219,] -1.540903396 -0.09859304 -1.1167612805 0.8029841934 -0.165862050
## [220,] 4.811125983 2.34468196 -0.3322754239 0.5855998508 1.125323479
## [221,] 2.960210184 0.25580109 -1.3532023514 1.1105279220 0.660503185
## [222,] 0.548555090 1.20673516 -0.5847280068 1.2403006951 -0.255814803
## [223,] -1.203818787 0.41491335 0.6516018979 -1.7888960008 -0.675920517
## [224,] -0.095903547 -0.65584776 -0.5358363119 -1.2541542670 0.075096599
## [225,] -1.447284264 -1.00724102 -0.6082703522 -1.5298781643 0.066886767
## [226,] -0.721456172 1.13787970 0.8467912909 -2.0802276689 -0.435596218
## [227,] 2.040310983 0.43242568 -0.2461052925 0.7423873284 -0.579002419
## [228,] 1.855207556 1.67633604 0.5148301396 -0.1260125667 -0.807029471
## [229,] -1.362709085 0.28203522 -1.2055884775 0.5729921576 0.186353531
## [230,] -0.288896751 0.20730044 0.2845176632 0.6308919312 -1.505210536
## [231,] -0.418601999 0.23532480 0.2238988269 -0.5027334058 -0.945826637
## [232,] -1.163850583 0.68497750 -0.8821849871 0.8863377110 0.002177941
## [233,] 0.411132602 1.16486925 -0.3493614654 1.3942763398 -0.698315265
## [234,] -1.693135796 -0.47771445 -1.0852001549 0.2466849979 -0.106371453
## [235,] -1.469262447 0.58168692 0.2179103849 0.0730339108 -1.083523772
## [236,] -1.241804213 1.79930936 0.0417415503 0.6900290082 -0.739436237
## [237,] 3.689808324 1.67054618 0.2271980354 -0.1712036874 0.320606604
## [238,] 0.637785394 -1.18641596 0.3164064662 0.3364686684 -2.013280789
## [239,] 6.741912903 1.29247340 -0.5420542885 0.4573219426 1.094774796
## [240,] -1.238593026 -0.23776840 -0.5949271348 -1.3969869040 0.325843132
## [241,] 0.823175506 1.06316740 -0.5254541417 -0.6645444043 0.438143394
## [242,] 0.046147404 1.10794300 0.9541899343 -1.0517974932 -1.112030077
## [243,] -0.926653518 -0.47703938 0.3584883210 0.7483755808 -2.030451588
## [244,] 1.642861658 0.76706108 0.4101327315 -1.6601340760 0.241603918
## [245,] 0.577872627 -0.27228218 0.0857683853 -1.3777634787 -0.319784341
## [246,] -1.754825326 0.80791517 0.5577871077 -0.0676093662 -1.377625236
## [247,] -2.038325012 0.13688760 -0.0003412363 0.3430358578 -1.217973430
## [248,] 0.534102452 0.42078510 -1.1547081981 -0.6235503927 0.941303310
## [249,] -0.778602587 0.16187841 -0.3007337578 -2.1397103069 0.556468021
## [250,] -1.358620602 -0.11871598 -0.0786250759 -1.0668656351 -0.441391917
## [251,] 0.552972231 -1.32892174 0.2653874378 -1.7448134449 -0.716425820
## [252,] 0.160512695 -1.07401603 -1.3645629081 0.1229912862 0.139386122
## [253,] -0.255760964 -1.55052571 -0.6215940219 -1.4389507212 -0.116189564
## [254,] 2.380048532 -1.22313608 -0.4828668231 -1.7734074221 0.293324720
## [255,] 2.562080786 -0.62564376 -0.7980444051 1.7530531164 -1.022362433
## [256,] -0.556325503 0.61870762 0.4208116759 0.5833612102 -1.567526425
## [257,] -1.361977024 0.48557037 -0.3780687286 -0.2263198361 -0.261824026
## [258,] -1.604168388 0.15729081 -1.1427967214 0.6878894786 -0.014904788
## [259,] 0.453544197 -0.10135935 -0.0830135546 -1.4480142567 -0.154195510
## [260,] -0.245088734 -0.21116664 -0.8071754259 0.2429511311 -0.279436645
## [261,] -0.586494355 0.59713665 -2.4100725243 -0.5973150226 2.411185160
## [262,] -0.595783004 -0.97017702 0.1712856607 -1.4091442191 -0.895962157
## [263,] -0.098509308 -0.71157736 -0.6190102919 -0.8101660640 -0.107118411
## [264,] -1.732739711 -0.01171917 -0.9714345094 0.9911466978 -0.385416176
## [265,] -1.312518153 2.21664937 1.0466799279 0.0855880150 -1.449625633
## [266,] -1.117483636 -1.07344208 -0.1309504223 0.5351107892 -1.625027906
## [267,] -0.802242010 2.43916871 -0.0658918448 0.5326247945 -0.249856505
## [268,] 1.779574174 -2.20525734 -1.2254437217 -1.4601618621 0.480018703
## [269,] -0.692885384 -0.50625416 -1.6109602188 1.2266062367 0.002189829
## [270,] -0.296827034 2.09903244 -0.5356781950 1.0212095064 0.236744458
## [271,] 2.648459041 -0.60314173 -1.1623236353 -1.1868983731 1.137440016
## [272,] -0.009329958 0.66837011 -0.6089249244 -0.0124265699 0.007020687
## [273,] 0.636626889 0.36453000 -1.0956031271 -0.4201642118 0.755836178
## [274,] -0.730329225 0.63180054 -0.2775908413 0.0076169716 -0.174167360
## [275,] 0.329127497 -0.70211196 -1.1270499206 -1.3794822582 0.788719121
## [276,] -1.859016837 -0.41444458 -1.0884680056 0.0004891493 0.032889030
## [277,] 2.011187895 -1.86028031 -1.4701740451 1.9592818340 -0.863881329
## [278,] 4.387657320 1.01990704 -1.0694317529 1.0313056985 0.910287718
## [279,] -1.562200265 0.50506920 0.3257902808 0.4071536855 -1.418071805
## [280,] 1.140064695 -0.84165314 0.0475366423 0.1828157194 -1.383731574
## [281,] -1.592089421 0.68980851 0.0241838972 -0.0763303675 -0.781020214
## [282,] -0.863852065 0.20642081 -0.8983962803 -1.0667886017 0.713765183
## [283,] 1.027169030 1.16456255 -1.0404846287 -0.0396471898 1.049317709
## [284,] -0.436517354 -0.42713213 0.0134409058 -0.8973018413 -0.722139204
## [285,] 0.337411799 -0.24417082 -0.6480989722 -0.0855047074 -0.227110796
## [286,] 0.922063650 -0.22614793 -1.9443047687 0.7895315305 1.017821370
## [287,] 0.074518204 0.02674638 -1.0857966267 0.5553685803 0.035340926
## [288,] 0.517903752 0.07720678 0.7802091323 -0.3889323964 -1.326401252
## [289,] 1.205633993 4.05992941 1.7774871852 0.5243784073 -0.779237256
## [290,] 5.667322803 1.41683162 0.5192606886 -0.5242010735 0.057913957
## [291,] 0.117634314 2.05280704 1.1202906141 -0.2225732744 -1.394044856
## [292,] -1.257776898 0.99085451 -0.6432249171 0.7239870280 -0.267413061
## [293,] -1.442594978 0.64860803 -1.1825132672 1.3464166771 -0.103965971
## [294,] 0.581815447 0.15948370 0.5111637426 -1.5852378542 -0.514462082
## [295,] 3.192976367 -0.80514579 0.6934590185 -0.6145019682 -1.279398203
## [296,] -1.664428065 0.44940153 -0.8138817842 0.9169350091 -0.409961580
## [297,] -1.381280799 -1.04718836 -0.8104653996 -1.2130194950 0.131190811
## [298,] -0.359580844 -0.02707621 -0.2139147820 0.7519546558 -1.081305483
## [299,] -1.295214100 0.90633579 0.3446284016 -0.9705650257 -0.587847432
## [300,] 1.275367360 -0.46955884 -0.9321790556 1.6880185073 -0.857351331
## [301,] 0.510190648 -0.47545309 0.1659852525 -1.4398287570 -0.586650046
## [302,] 0.497692443 0.73632621 -0.7320867366 -0.6396358886 0.543145415
## [303,] -0.360524908 1.94049135 -0.0814679929 -1.0578009624 0.492777950
## [304,] 0.680162177 4.39853961 1.3939873156 -0.0903894719 -0.359689359
## [305,] 0.651993920 1.46566547 -0.5054646735 1.4206026417 -0.393377040
## [306,] 3.788964776 -1.08829199 -1.2835697130 1.5189289232 -0.160003180
## [307,] 0.324102302 0.44636919 -0.0358560470 -1.7147746806 0.185602167
## [308,] 1.241627938 -0.80113200 -0.9370602561 0.5736384332 -0.380036721
## [309,] -0.511968929 -1.17458566 -0.6546640582 -0.3823368294 -0.528559592
## [310,] 0.718039754 0.17733890 -0.6884966946 -1.2988653722 0.666658316
## [311,] -0.310163020 -1.06311682 -0.8411613032 -0.3440185709 -0.239649145
## [312,] -1.033055205 1.28803157 -0.7885399882 1.0583019502 -0.014148637
## [313,] -0.764852259 0.84975776 -0.4166580478 -0.3570104900 0.163850456
## [314,] 2.840965510 1.27703956 1.2737033558 -0.0712572107 -1.299150219
## [315,] -1.178758036 -0.07789715 -0.1547232721 -1.1892312531 -0.258297637
## [316,] -0.802177079 -0.95036649 -0.6926590212 0.0641135168 -0.653215774
## [317,] 1.938258838 -1.28408318 -0.7550485265 -0.2456973992 -0.386044302
## [318,] -1.084340607 0.56509571 -0.3641566428 -0.4657496728 -0.069947785
## [319,] 5.007927517 1.33213703 0.4628978606 -0.6412930066 0.335503981
## [320,] -0.352175349 0.05184295 -1.0595996323 1.1419351290 -0.354514092
## [321,] -1.645893870 0.67772347 0.5678664419 -0.6516041624 -1.130232840
## [322,] -0.723629619 0.28418574 -0.9155428645 -1.7398043966 1.090294733
## [323,] 2.150497872 -1.85335253 -0.9536747162 -0.9930159522 0.090967074
## [324,] 0.219479185 0.70653560 0.4625353948 0.0635989317 -1.095438714
## [325,] -0.347437994 0.13601327 -0.3616040070 0.0995137840 -0.602584780
## [326,] -0.234908136 0.38370796 0.3810829977 0.2955102824 -1.313248723
## [327,] 0.016559745 -0.24813137 0.3418529439 -0.6289931873 -1.073354029
## [328,] -1.467247701 -0.93657939 -1.0073778050 -1.3484920808 0.464904725
## [329,] 1.154836707 -1.65839860 -0.1796696786 0.5786916927 -1.773817068
## [330,] 0.020892606 0.14389944 0.1408600742 0.1842691926 -0.953519579
## [331,] 0.169022729 0.24173475 0.6782816134 -1.3801420819 -0.971815989
## [332,] 0.596241854 0.70051500 -1.8052088015 -0.0053918173 1.465700551
## [333,] -1.658882001 -0.32657130 0.2318064743 -0.3636469103 -1.209182254
## [334,] -1.130296134 0.92484749 -0.3380519552 -0.3013039197 -0.112208131
## [335,] -0.114349001 -0.27920208 -0.6403335111 -0.2074405468 -0.257747260
## [336,] -1.180178802 0.03183833 -0.3500656477 -1.0972084429 -0.005358715
## [337,] 1.016962553 -1.84125842 -1.0359966156 0.1725787385 -0.567197423
## [338,] 1.874901202 -1.13532877 -0.6093993174 1.0930613053 -1.160229327
## [339,] -1.674481841 0.44986836 2.1646104925 0.9678148811 0.135461099
## [340,] 0.347838749 -0.88857174 0.8771393702 -0.0399280185 1.772672225
## [341,] -0.523787799 -0.92658682 1.5418929659 0.1325485002 0.785980424
## [342,] -1.191298001 1.23405600 1.7890495622 1.3692564275 0.892653715
## [343,] 1.808772263 -1.69685692 0.8907964331 -0.2029722962 1.489618576
## [344,] -1.770065768 -0.81617964 1.3539885104 -0.2766980579 1.166492368
## [345,] -0.206433118 0.56197089 1.8053747930 1.3814075643 0.495893161
## [346,] 0.781356058 -0.26730308 1.4981375832 0.8043655618 1.134248369
## [347,] -1.821829245 -1.41978625 1.5929954355 -0.6929508188 0.865846962
## [348,] -0.284787326 -0.98055909 2.0711730642 -0.3625595662 0.392274537
## [349,] -0.436832085 1.81979653 1.9654352950 0.0409412675 1.657960929
## [350,] -1.217940564 -0.03242505 1.5341269350 0.0689673368 1.157904466
## [351,] 1.408443279 -0.92755403 2.5527909101 -0.6932672647 0.150225917
## [352,] 0.076806137 -0.36230781 1.0569801425 0.7081503355 1.356282603
## [353,] -1.371613972 -0.73826316 -0.0390647200 0.5827617423 2.417181597
## [354,] -1.864312777 -1.17836386 1.6190160585 -0.8239266507 0.990897877
## [355,] -1.989259900 -1.78295952 1.5112558257 -0.6883823148 0.805384073
## [356,] -0.666931670 0.04442279 0.9603229118 1.9679277491 0.821582895
## [357,] -0.752021652 0.57932223 1.1919215542 0.0297044937 1.852331941
## [358,] -0.799705965 -1.07103612 0.3748144882 2.1390626788 1.010092176
## [359,] -1.601727166 -1.41026284 0.7915067164 -0.2584759327 1.601877583
## [360,] -1.657122757 0.50517962 1.7207936026 1.3778309508 0.405279647
## [361,] -0.384493964 -0.88081329 0.5179378168 0.9525680456 1.560400572
## [362,] -1.117824446 0.07013439 2.3329630062 -0.8981794794 0.738754653
## [363,] 2.156938592 -0.59054334 0.9679981313 1.4564801625 1.063503699
## [364,] -0.789754021 -2.12761614 1.4729430325 0.0219314842 0.410727684
## [365,] -1.380570918 -1.02926654 1.9974600705 -1.3875631548 0.968366183
## [366,] -1.291560292 0.38334086 1.4160677141 1.5258026469 0.762317564
## [367,] -0.935262338 0.56231264 2.1242791830 0.3720182728 0.718006182
## [368,] 2.492171120 -0.48928746 2.4676282836 1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614 2.2688783371 0.9603180211 -0.407816836
## [370,] -1.468296601 0.18028669 1.6652393313 1.5773153771 0.412661443
## [371,] 0.644477407 1.35334644 2.6883609615 0.5712489712 0.440528158
## [372,] 4.369563022 -1.66481832 1.6865361527 0.4901972904 0.760040778
## [373,] -2.357052820 -1.26900605 1.5231357317 1.0301102498 0.074632682
## [374,] 0.718708019 0.22127710 1.0354060443 0.2583339391 1.891779073
## [375,] 1.391878059 0.98004221 1.7111474295 -0.7952838709 2.265775349
## [376,] 0.905097897 -0.22694710 2.1140189340 0.5476029310 0.603860387
## [377,] 3.157230391 -1.19754195 1.1484347290 1.0599855046 1.186962665
## [378,] 0.003135705 -0.90598915 1.6393299343 -1.1011824448 1.359035590
## [379,] -0.242056357 -0.73255189 1.7021620290 -0.1866470103 0.800865246
## PC6 PC7
## [1,] 0.814428206 -0.107883916
## [2,] -0.048912344 -0.099604504
## [3,] -0.086507916 -0.138527863
## [4,] -0.822748232 0.360506834
## [5,] -0.108812986 0.078970882
## [6,] 0.183797925 0.433343571
## [7,] 0.008911379 -0.004657966
## [8,] 0.543125568 -0.332707934
## [9,] -0.752701863 0.056474342
## [10,] -0.441826427 -1.924448799
## [11,] -0.244944687 0.159851097
## [12,] 0.206259597 -0.169273224
## [13,] 0.163519054 -0.103667561
## [14,] 0.132474346 0.108653816
## [15,] -1.324055932 -0.183915616
## [16,] 0.714919089 0.304537991
## [17,] -0.647376538 0.365592105
## [18,] 1.097596271 -0.377715183
## [19,] 0.334391075 -0.234827285
## [20,] 0.808587321 -0.200036177
## [21,] 0.322170368 -0.166529357
## [22,] 0.107803508 0.012805983
## [23,] -0.332323319 -0.202474142
## [24,] 0.995998868 0.201016672
## [25,] -2.363493528 0.266625584
## [26,] -0.813907073 -0.571488560
## [27,] -2.160783056 0.281527887
## [28,] 0.098479393 0.336756957
## [29,] 0.004273460 -0.381406184
## [30,] -0.044211599 -0.418300721
## [31,] -0.128464996 0.054899611
## [32,] -0.357344175 0.183909490
## [33,] -0.597244606 0.289672968
## [34,] 0.259235600 0.349194654
## [35,] -0.236888897 -0.371166651
## [36,] -0.249251785 0.050335461
## [37,] 0.607590347 -0.462113845
## [38,] -0.026797156 0.355817879
## [39,] 0.166045669 -0.073826942
## [40,] -0.162738506 -0.392300116
## [41,] -0.522507663 -0.121724380
## [42,] 0.067225848 0.209115377
## [43,] -0.417780877 -0.474060203
## [44,] -0.173878940 -0.457967209
## [45,] -0.050403121 -0.134114068
## [46,] -0.089979747 -0.491479393
## [47,] 0.480573605 -0.072323181
## [48,] 0.228887831 0.155522234
## [49,] -0.489991807 -0.227097997
## [50,] -0.606582969 -0.101166456
## [51,] 0.577660866 -0.455756839
## [52,] 0.585446120 -0.388137976
## [53,] 0.734811073 1.561539615
## [54,] 1.381511548 0.252947237
## [55,] 0.358959045 -0.182311216
## [56,] 0.207910788 0.078632864
## [57,] 0.607774154 -0.281869942
## [58,] 2.443161543 0.443513680
## [59,] 0.206843192 0.253038172
## [60,] 0.135499206 0.164773439
## [61,] 0.648725932 0.351461678
## [62,] 0.166486526 0.246682271
## [63,] -0.513948300 -0.286040883
## [64,] 1.163578265 0.263125274
## [65,] -0.009862807 0.134046265
## [66,] -0.730377136 0.337181681
## [67,] -1.487448857 -0.149925371
## [68,] 0.220853759 0.272493773
## [69,] -0.588054260 0.260689981
## [70,] -0.385273067 0.319508713
## [71,] -0.175254751 1.897246402
## [72,] -1.300330063 -0.404208363
## [73,] 0.816322549 -0.225387244
## [74,] -0.060212427 0.165026305
## [75,] -1.649589162 -0.529795744
## [76,] 0.569158827 -0.263377372
## [77,] -0.165692949 -0.401192949
## [78,] 0.043436354 0.440699177
## [79,] 0.327782857 0.371732847
## [80,] 0.016945132 0.140928440
## [81,] -0.877693420 -0.271276638
## [82,] 0.050656761 0.314869348
## [83,] 0.024270266 -0.489647178
## [84,] -0.428408376 0.144447332
## [85,] 0.302353058 0.176709283
## [86,] -0.930367776 -0.038966156
## [87,] 0.206974359 1.518547012
## [88,] 0.773220076 0.387655208
## [89,] -0.057425863 0.311702214
## [90,] -0.319492539 -0.104439493
## [91,] 0.464021241 -0.182053564
## [92,] 0.568469956 0.135273025
## [93,] -0.637098352 -0.352179961
## [94,] -0.897710356 -0.603436508
## [95,] -0.302718373 0.134220300
## [96,] 0.796303291 -0.453234619
## [97,] 0.102248374 -0.373850042
## [98,] 0.276775028 -0.386841666
## [99,] -0.147547074 -2.150145655
## [100,] 0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,] 0.945355253 0.288290374
## [103,] 0.240503118 0.089283023
## [104,] 0.040655927 -0.326527188
## [105,] 0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,] 0.617517671 -0.018331347
## [108,] -0.140360458 0.357139007
## [109,] -0.369058053 -0.363453154
## [110,] 1.367651547 -0.052494633
## [111,] -0.245674045 0.171961839
## [112,] -0.288279169 -0.437854120
## [113,] 0.654181743 0.335734007
## [114,] 0.430171258 0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461 0.293451739
## [117,] 0.435961104 0.348338090
## [118,] -1.122876095 0.371334968
## [119,] 0.128953459 -0.002950892
## [120,] 0.454338848 -0.320002000
## [121,] -0.393321862 0.002244332
## [122,] 0.694427666 -1.776651924
## [123,] -1.480360092 0.237363812
## [124,] 0.563305776 0.061168635
## [125,] 0.789672355 0.182676841
## [126,] 0.657430786 0.151394277
## [127,] 0.052053042 -0.260063201
## [128,] -0.509971776 0.300299579
## [129,] -0.514688913 0.253498821
## [130,] -0.230653718 0.334001823
## [131,] 0.234492897 0.070164155
## [132,] -0.509623760 0.211476411
## [133,] -0.508032972 0.218820879
## [134,] -0.584676128 0.432040803
## [135,] -0.599512631 0.114578050
## [136,] 0.742555446 0.264941606
## [137,] 0.215593238 -0.296341138
## [138,] 0.814373445 -0.463329220
## [139,] -0.705236433 0.235224585
## [140,] -0.240819937 0.128832004
## [141,] -0.738265473 0.045748305
## [142,] -0.516065685 0.423763629
## [143,] 1.032627703 0.255695270
## [144,] 1.011640901 -0.046612704
## [145,] 1.036057364 -0.116502648
## [146,] 0.238779557 -0.094409829
## [147,] 0.093045275 -0.025943269
## [148,] -0.018285774 0.063985702
## [149,] -0.821062597 0.316957388
## [150,] -0.051433159 -0.325889337
## [151,] 0.240258258 0.157499206
## [152,] 0.244055313 -0.484326189
## [153,] 0.321762278 0.347844280
## [154,] -0.688031620 0.275674116
## [155,] 0.052870105 0.278750325
## [156,] 0.259394959 0.994613529
## [157,] 0.384573263 0.255112420
## [158,] -0.647167228 0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,] 0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636 0.354791023
## [164,] 0.259528832 0.196856471
## [165,] -0.112837907 -0.422270866
## [166,] 0.128000241 -0.175939627
## [167,] -0.895512404 0.337192272
## [168,] -0.711019273 -0.814804273
## [169,] 0.218357219 -0.033915231
## [170,] -0.078144315 0.263676922
## [171,] 0.789052948 0.069697557
## [172,] 0.334044498 0.095799549
## [173,] -0.466799910 0.182242801
## [174,] -0.409218588 0.105315011
## [175,] 0.475675622 0.157100174
## [176,] 0.631970192 -0.312887516
## [177,] -0.842796008 0.184336624
## [178,] -0.521271064 0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439 0.339455192
## [181,] 1.224469205 0.162311433
## [182,] 0.896759582 -0.187133556
## [183,] -0.369525579 0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790 0.938668397
## [186,] 0.115704613 -0.308573611
## [187,] -0.330011041 0.052298230
## [188,] 0.252831722 -0.344500770
## [189,] 0.478267892 -0.411989559
## [190,] 0.108389410 0.270176494
## [191,] 0.320051815 -0.452948617
## [192,] -0.927317654 0.050049377
## [193,] 0.049967323 0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643 0.112196595
## [196,] -0.426323754 0.064708147
## [197,] 0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,] 1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,] 0.222523935 -0.327353336
## [202,] 0.143637470 -0.384469784
## [203,] -0.685873899 0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209 0.286336764
## [206,] -0.391145161 0.071275723
## [207,] 1.031184262 -0.071523474
## [208,] 0.422795216 -0.361912372
## [209,] 0.232252275 -0.321891385
## [210,] 0.132512399 -2.194006418
## [211,] 0.300407101 0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275 0.013076856
## [214,] -0.146543860 0.258375350
## [215,] -0.914443039 -0.156858207
## [216,] 0.163052914 0.373094641
## [217,] 0.735902331 0.298434341
## [218,] 0.858016687 -0.410620478
## [219,] -0.698483214 0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,] 0.103014117 -0.154551366
## [223,] 0.032313480 0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311 0.316447811
## [226,] 0.757677018 0.355289619
## [227,] 0.112343498 -0.370694673
## [228,] 2.840081863 -0.472760040
## [229,] -0.117535015 0.251369052
## [230,] -0.123999729 -0.103219333
## [231,] 0.620151206 -0.398726087
## [232,] -1.258499518 0.031686285
## [233,] 0.508788077 0.031702502
## [234,] -0.730990134 0.229897436
## [235,] -0.131943879 0.351750927
## [236,] 0.930178961 0.218030323
## [237,] -1.155883577 -0.406938969
## [238,] 0.421016873 -0.245001577
## [239,] -0.919968833 0.339656927
## [240,] -0.475488496 0.136247856
## [241,] 1.761754259 0.029538972
## [242,] 1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019 0.116533237
## [246,] 0.123274608 0.151123503
## [247,] -0.489960306 0.098338159
## [248,] 0.676566199 -0.339944716
## [249,] 0.072286130 0.262572292
## [250,] -0.203974262 0.359934672
## [251,] -0.962511140 0.447744836
## [252,] 0.026617023 0.293556296
## [253,] -0.615601226 -0.158798853
## [254,] 0.165313198 0.013008846
## [255,] 1.432136191 1.223639292
## [256,] 0.483977624 -0.346520349
## [257,] -0.153805545 0.159416002
## [258,] -0.327177547 0.145372443
## [259,] 0.927279628 0.136024542
## [260,] 0.347645497 -0.209884830
## [261,] 0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891 0.117204649
## [265,] 1.233710972 0.172803485
## [266,] -0.621049559 -0.266818669
## [267,] 1.556396291 0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685 0.155867363
## [271,] -0.136040334 -0.327359471
## [272,] 0.778990215 -0.465309183
## [273,] 0.693723928 -0.130197667
## [274,] -1.468695169 0.266972231
## [275,] 0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,] 0.336674762 1.064820895
## [278,] -0.300804152 0.703841870
## [279,] -0.238262975 0.450690335
## [280,] 0.395969716 -0.242043012
## [281,] 0.109021256 0.138748544
## [282,] -0.037963898 0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,] 0.426625104 0.228719436
## [286,] -0.362288537 0.223311049
## [287,] 0.384277844 -0.106878993
## [288,] -1.421668738 0.046595855
## [289,] -2.984199195 0.075859453
## [290,] 1.319916883 2.001667923
## [291,] 2.046793198 -0.269649215
## [292,] 0.392813424 0.303644436
## [293,] 0.021688217 0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153 0.163389864
## [297,] -0.811118093 0.416648260
## [298,] -0.340865035 -0.224224889
## [299,] 0.466059600 0.157785884
## [300,] 0.558304051 -0.192471657
## [301,] 0.750653613 0.459663166
## [302,] 1.122352945 -0.276052847
## [303,] 1.078964668 0.210264826
## [304,] 0.426300512 0.141513828
## [305,] 0.810547774 0.065859782
## [306,] -0.181814543 1.697357273
## [307,] 0.699571022 -0.449062901
## [308,] 0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,] 0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323 0.125575320
## [313,] -0.600269847 0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717 0.438769076
## [316,] -0.386407008 -0.406110560
## [317,] 1.041640267 0.390303651
## [318,] -0.189857024 0.234508553
## [319,] -1.090183460 0.762300322
## [320,] 0.386282802 -0.239807387
## [321,] 0.134404520 0.127105246
## [322,] 0.366835108 0.216268360
## [323,] 0.342909111 0.372677157
## [324,] -0.254516438 -0.193658003
## [325,] 0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346 0.003333250
## [328,] -0.798713796 0.164392019
## [329,] 0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,] 1.020308661 0.044230674
## [332,] 1.056394345 -0.394589336
## [333,] -1.007313550 0.374213944
## [334,] 0.492601789 0.244276984
## [335,] 0.411613111 -0.135788109
## [336,] -0.280767946 0.263720304
## [337,] 0.160862506 -0.192753984
## [338,] 0.791036742 0.678047807
## [339,] 0.126529280 0.120748763
## [340,] 0.262317102 -0.088849352
## [341,] 0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,] 1.445310485 0.036985630
## [344,] -0.175915279 0.027902348
## [345,] 0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184 0.213624141
## [348,] 0.448319463 -0.109057231
## [349,] 0.164185074 -0.178027089
## [350,] 0.343302649 0.295711308
## [351,] 1.064600476 -0.399557062
## [352,] 0.402428026 -0.264910522
## [353,] -0.039235833 0.080955691
## [354,] -0.401278508 0.033682397
## [355,] -0.845062983 0.190359077
## [356,] 0.916027349 -0.545821754
## [357,] 0.946629462 0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729 0.232244290
## [360,] 0.620269650 0.217072532
## [361,] 0.290272477 -0.446292100
## [362,] 0.807055770 0.427223893
## [363,] 1.725250067 0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260 0.310782840
## [366,] -0.025556816 0.310309937
## [367,] -0.369535370 0.246732337
## [368,] 0.794924538 0.929445109
## [369,] -0.044906053 0.144701045
## [370,] -0.730353345 0.202922032
## [371,] 0.105639703 -0.429239913
## [372,] -0.245135971 0.186120856
## [373,] -0.823120736 0.174853047
## [374,] 1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214 0.135743929
## [377,] -0.299503313 0.743333133
## [378,] 0.410392839 -0.361555114
## [379,] 0.837670932 -0.196874004
Cancer_pca$rotation[,1]
## Age Stage Tumor Size
## -0.21487519 0.56017028 0.57902017
## Regional Node Examined Reginol Node Positive Survival Months
## 0.23910247 0.45785153 -0.18008353
## Sex
## -0.07446786
Cancer_pca$rotation
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional Node Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol Node Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6 PC7
## Age -0.41336263 -0.03629602 -0.00410619
## Stage -0.21766761 0.18269976 -0.69082826
## Tumor Size -0.13361696 0.13694401 0.71864375
## Regional Node Examined -0.03947383 0.57624593 0.00365182
## Reginol Node Positive 0.10540722 -0.76394463 -0.04789123
## Survival Months -0.63971799 -0.15748760 0.05900235
## Sex 0.58479969 0.07795267 -0.02241484
Cancer_pca$x
## PC1 PC2 PC3 PC4 PC5
## [1,] -1.441559363 1.84595445 -0.3691842456 0.8313546497 -0.332307184
## [2,] 0.466697152 0.06803649 -0.6236808487 -0.3679040103 0.110810520
## [3,] 1.724644704 -0.46933933 -0.1593826887 0.5351088884 -1.007021612
## [4,] -1.727412749 -0.67153366 -0.6471303735 -0.0657071859 -0.534587533
## [5,] 0.084534880 -1.24252757 -1.5702796993 -0.3040439925 0.527096385
## [6,] -0.987174108 0.58301426 0.1669091720 -0.9999683133 -0.430923510
## [7,] -1.289312885 0.33343114 -1.1225709379 -0.4660831193 0.647838054
## [8,] 0.457476281 -0.43703336 -2.3348237400 -0.5798103154 1.901144959
## [9,] 5.013544810 -0.35127563 0.3138865965 -0.6789485742 -0.346406933
## [10,] 1.966110970 0.57900951 0.8436785098 1.1971488330 -2.024615276
## [11,] -1.709742154 0.39272616 -0.8797546127 1.0395229446 -0.421546565
## [12,] 1.323214712 -1.40692828 0.0010448762 -0.8532983622 -0.998148360
## [13,] -0.047344848 0.20982069 -0.8615166802 1.1288786920 -0.430771477
## [14,] -0.023379894 1.83512622 -0.8543600804 -0.5919635549 1.267459198
## [15,] 1.042993427 1.19479846 -0.1106365956 0.7578922926 -0.309831792
## [16,] -0.954171084 1.25373181 -0.8631921253 0.4922727293 0.235344753
## [17,] -0.510183493 -1.74284660 -0.1083044907 -0.2184460954 -1.466753080
## [18,] 0.248390384 0.43156365 -0.4623851738 -1.2333483190 0.363615703
## [19,] -0.386424810 -0.37494859 0.5477775527 -1.3442739171 -1.122742523
## [20,] -0.212235416 0.44848661 -0.0814638947 0.1978257208 -0.848560671
## [21,] 0.001291199 -0.22401731 -0.1753398416 -0.9042251252 -0.381745196
## [22,] 0.547237523 0.35323566 -0.8945832960 0.4857434118 0.105717976
## [23,] -0.581794885 -1.07033107 -0.7283097731 -0.0629010628 -0.572677371
## [24,] 1.484574719 -1.12275223 0.4930197218 -0.8534326311 -1.510109489
## [25,] 0.730385134 3.01009366 1.5328340955 -0.0845516282 -0.807050880
## [26,] 1.384044724 2.86730858 0.7935319092 0.4879719811 -0.466990302
## [27,] 2.503197607 1.86942247 1.6035708576 -1.0898911376 -0.702827024
## [28,] -1.094732396 0.13919430 -0.2430526831 -1.3348711724 0.009704223
## [29,] -0.040233637 0.24894946 -0.5823916977 0.1870202613 -0.228150297
## [30,] -0.913495245 -0.27255918 -0.2249052502 0.7136559763 -1.283048492
## [31,] 0.044817272 -1.24749459 -1.5147400984 -0.3403352312 0.475434709
## [32,] -1.310023914 -0.18810081 -1.5041631045 -0.0748728835 0.691915088
## [33,] -1.750326793 -0.31441971 -0.3126381565 -0.1365620557 -0.754412318
## [34,] -0.860691537 1.17774354 -0.4731321013 0.2383866081 -0.049714847
## [35,] 1.293140200 1.12837700 -1.0955034983 -0.3513923420 1.283108823
## [36,] -1.575412171 -0.65517742 1.1178980897 -0.0145585733 1.416899251
## [37,] 0.505620687 0.48204717 0.6768751198 0.9826148200 2.080438807
## [38,] -1.445729993 -0.53420180 2.0397881463 -0.4191403509 0.606045480
## [39,] -0.240634131 -1.38008841 1.2981310791 0.0234566336 0.948153836
## [40,] -0.335231355 -0.71567154 2.2622815166 -0.2598837684 0.304358552
## [41,] 2.392046521 -0.75381886 0.6808155988 1.7849935943 1.462378918
## [42,] -1.496209472 -0.05147919 0.8362058172 1.4463882147 1.234755769
## [43,] -1.238156754 -1.73396163 1.0838915624 1.1966166369 0.342914980
## [44,] -0.122858339 -0.41520397 1.7259286489 0.2467343049 0.834734733
## [45,] -1.614959830 -0.21262796 0.8270352673 0.5084458503 1.653782254
## [46,] 0.653344872 -1.45282335 1.6923961454 1.7730389364 -0.346353752
## [47,] -0.903132282 0.00288121 0.2891894480 -0.3828977838 2.883679498
## [48,] -1.570956435 -0.13307164 0.7378711359 1.2691205943 1.372131721
## [49,] 0.407142180 -0.18484286 1.8224576827 0.3406571927 0.900265041
## [50,] -2.095133885 -0.24603762 1.3075254314 1.5865972660 0.515650798
## [51,] 0.145196356 -0.72051716 1.2885099274 -1.1072761596 1.854988517
## [52,] 0.438754344 -1.67207421 0.9831353778 2.3512915236 -0.039137939
## [53,] 2.005777230 -2.95342227 1.2688959631 1.7356814675 -0.406467811
## [54,] 1.526981600 -1.02119752 1.4223445513 1.8001650835 0.106389455
## [55,] -1.762004433 0.13389155 1.3060891880 0.4365138287 1.220327765
## [56,] -1.584099552 -0.27233552 1.1461680461 0.3643457178 1.304773967
## [57,] -0.496130040 0.33490544 0.2711418287 0.1648088615 -1.311783436
## [58,] -0.310631363 3.07311289 1.8743230894 -1.7983452746 -1.034356670
## [59,] -1.133478035 0.41599332 -0.4379284603 -0.8528069490 0.092369673
## [60,] -1.203472671 0.78226143 -0.1914939617 -0.4844823758 -0.219974275
## [61,] -0.899762531 1.31926126 0.1811318594 -0.4938217806 -0.418037102
## [62,] -1.006446958 0.35539993 -1.2221294160 -0.3469217710 0.736595283
## [63,] -0.437812701 -1.58636590 -0.8897438306 -1.2595916576 0.044579623
## [64,] 1.712300783 -0.45593265 -0.1013381728 0.5911078860 -1.251280484
## [65,] -1.263885916 1.17224839 -0.6291534095 0.9206949813 -0.255173442
## [66,] -1.604219653 -0.82712464 0.0494208809 -1.5797529143 -0.620332594
## [67,] 4.488026052 1.14176192 -0.1231038156 -1.5112898673 1.345935978
## [68,] -0.665172931 0.68451038 0.1453995807 -2.0258292592 0.217431325
## [69,] -1.668377900 -0.33091730 -0.6606673180 -0.0526400595 -0.390248550
## [70,] -1.130422629 0.23695569 -0.1769384999 -0.7612337767 -0.266397542
## [71,] 3.316812797 -1.81535426 0.5502180418 -0.2694003925 -1.764262412
## [72,] 2.172380940 2.85911092 -0.9844345887 1.6403461146 1.175874251
## [73,] 0.572326326 -0.34757898 -1.0234096521 -2.0869344002 1.187096201
## [74,] -1.827615023 0.62057292 0.3016558087 0.2426806849 -1.315635893
## [75,] 0.720276568 1.70219107 0.6872975038 0.8005007414 -1.037240682
## [76,] 0.849193077 -1.14260361 0.1217975270 -0.0272015985 -1.564340163
## [77,] -0.640547040 -0.61272303 1.3854969929 1.5959470836 0.358667424
## [78,] -0.095120639 -2.25942107 1.7743414136 -0.8570595769 0.490508151
## [79,] -0.045215749 -1.67214619 1.1930256589 0.3311124134 0.788844783
## [80,] -1.769164273 -0.22777378 0.5215512977 1.9330657865 1.230687259
## [81,] 0.718379560 0.42702578 2.7049430509 0.0009902972 0.427134177
## [82,] -1.678008963 -0.30727716 0.8345249461 1.7090923528 0.957971947
## [83,] -0.895860760 -0.84819969 1.0351097886 1.6955225348 0.543187444
## [84,] -1.627068924 -1.17405222 0.1883777552 0.6241466387 1.941501550
## [85,] -1.331489281 -0.34160016 0.9121167916 0.1344506975 1.691751149
## [86,] 0.909892498 -0.53731582 1.4060161653 -0.0311065615 1.547734256
## [87,] 2.680823986 -2.87516871 1.2736995009 0.6959415006 0.332021211
## [88,] 1.353531002 -2.37316783 1.3254482077 0.7127875562 0.214693076
## [89,] -1.678967186 -0.70552936 1.6695940259 0.1038284595 0.653638646
## [90,] -2.304099591 -0.48981820 1.6210427235 0.9780934643 0.289061393
## [91,] 0.741204117 -2.34543537 1.4452706433 0.5998522096 0.088681106
## [92,] -0.809147683 -0.48805441 0.7203787577 -1.4686194537 2.727281577
## [93,] -0.790428226 -1.28394744 1.3498973595 1.2856985141 0.289629154
## [94,] 1.549314451 1.05942412 1.1109895492 0.1457696503 2.619577831
## [95,] -1.647991336 -0.27927996 1.6891990873 0.5048525410 0.651509510
## [96,] -0.268121798 -0.13194343 0.7385162603 1.3684964706 1.386087535
## [97,] -0.103534223 -1.33945241 -0.5191543874 1.0167737783 2.587808079
## [98,] -0.776307350 -0.99454099 1.0504553950 1.2109563269 0.697921783
## [99,] 1.103113756 -1.77799849 -1.0931648334 -0.0122323381 -0.394650374
## [100,] -0.409442426 0.35492707 -1.0502000077 1.4204609639 -0.397600387
## [101,] 4.633190126 2.16526818 0.6239105977 -1.1366907435 0.716197325
## [102,] -0.740349810 1.21149156 -0.0348952140 -1.2669488699 0.172769662
## [103,] 0.704221402 -1.11279489 -2.7553374907 -0.4028612238 2.065387989
## [104,] -0.385204834 -0.52764189 -1.2886177272 0.4419425766 0.047208371
## [105,] -0.068793640 0.07508422 -0.6067830446 -0.3162015548 -0.041201539
## [106,] -0.692576410 -0.91636560 -1.3471231484 0.7054513599 -0.195224769
## [107,] 0.345220609 -0.15476507 -1.9375149484 0.6213467649 0.919975929
## [108,] -1.364096376 0.64909093 -0.7204212843 1.0498159217 -0.453733562
## [109,] -0.387521866 -1.16290394 0.1995560232 -2.1751452860 -0.561207544
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## [112,] 1.210180885 -2.10091879 -0.7122063654 -1.4443151802 -0.137991722
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## [126,] -0.863182056 1.24685123 -1.9912585523 1.1497711812 1.220471619
## [127,] -0.118572831 -0.70053670 0.2417380654 -2.0356708316 -0.481456587
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## [144,] 0.505611656 1.09999711 -0.8457725436 0.9361832967 0.038535375
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## [146,] -0.602802743 -0.23260921 0.5437161698 -0.0788003168 -1.731152433
## [147,] -1.272341157 0.63788399 0.2396679916 -1.6177473606 -0.203905033
## [148,] 2.651497970 -0.83742214 -0.8602918415 -0.9187276925 0.528132953
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## [159,] -0.656681669 -1.17053344 -1.0085651375 -0.1509452878 -0.245449969
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## [161,] 0.576848393 1.03248254 -1.8769456788 1.1403757019 1.148244806
## [162,] -1.591129974 -0.30100995 -1.4737482868 -0.1586928611 0.631200467
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## [164,] -1.257058960 0.98743371 0.2695795040 -0.5173988569 -0.667657584
## [165,] 0.171012852 0.73662045 -0.6335336460 0.6662455703 -0.148260447
## [166,] 0.763873736 -1.48595671 -1.3893183822 1.8933152957 -0.923231546
## [167,] -0.648233872 0.65902369 -0.3523707692 -0.3496173059 0.053036529
## [168,] 4.075761272 -0.02211354 1.3258187920 -1.7139363992 -0.985583605
## [169,] 0.108096807 -0.74362678 -1.3323697664 -0.3209218040 0.450579099
## [170,] -1.498040609 0.19056435 0.2761281170 -0.9725452192 -0.798104332
## [171,] 0.047885996 0.72229011 -0.4345521427 1.3431830404 -0.865118234
## [172,] 1.337596168 -0.99890019 -0.4764831468 1.0952509419 -1.281949522
## [173,] -1.358485537 -0.11022223 -0.3457867052 -1.0397848770 -0.109872739
## [174,] -1.872027381 0.13432597 -0.2581474106 0.2022369490 -0.831155436
## [175,] -1.311243234 1.36865781 0.6373415177 -0.4090917149 -1.011660986
## [176,] 1.309706033 -1.47375458 -0.5852915698 -1.0931889293 -0.278496918
## [177,] -0.190859319 1.67724390 -0.7080844449 0.4280689948 0.590243975
## [178,] -1.150520519 -0.39541176 -0.6403158755 -1.4507416448 0.354044928
## [179,] 1.562083350 2.47954880 0.2323943105 -0.3200123444 0.378480572
## [180,] 0.457663612 -0.14582329 -0.6638729701 0.7733241568 -0.509222553
## [181,] -1.138195339 2.01560621 0.8465374351 -0.4823983801 -0.986316252
## [182,] -0.007740653 0.82444862 -0.0002346095 0.3074323320 -0.807425073
## [183,] -1.442466409 0.10416344 -2.2744315999 1.2646597948 1.004394643
## [184,] 1.401099127 0.69145106 -0.3432001965 -0.4552169029 0.392406398
## [185,] 3.044609211 -0.84163842 0.2359688651 -0.0030339038 -1.095598605
## [186,] -0.608848019 0.10718396 -0.0234540132 0.6904571295 -1.303809693
## [187,] 0.869481448 -1.63077965 -0.5698543214 1.5434401088 -1.685405103
## [188,] -0.300778748 0.05603470 -0.4615545760 0.1636332520 -0.514773465
## [189,] 0.636747830 2.30234603 1.1644239379 0.0093990323 -1.179875943
## [190,] -1.117892469 0.18858115 -0.3253204166 -1.3032488160 0.106289330
## [191,] -0.433517740 -0.06760578 -0.8846842302 0.3292279071 -0.195203996
## [192,] -2.074508151 -0.53753951 -0.4998051808 -0.0243119417 -0.707539233
## [193,] -0.943857160 1.31427799 -0.3177697220 0.3467708448 -0.211477339
## [194,] -0.671437346 -1.01840193 -0.5258171064 -0.3862781611 -0.631526388
## [195,] 3.146400023 -0.15766658 -0.4540461596 -0.5782133325 0.335024707
## [196,] -1.646968799 0.07418381 -1.4456195095 0.8218169329 0.234350644
## [197,] 0.194381857 0.17982364 -0.8329361597 0.1578319644 0.012979177
## [198,] 1.355794604 -1.31217975 0.2126240281 -0.5341546811 -1.308712601
## [199,] 0.342080981 0.71442970 -0.6482593800 -0.2099015734 0.202983167
## [200,] -0.390007297 -0.72256040 0.2659366383 -1.3023370226 -0.917914031
## [201,] -0.278709707 -0.06166132 -0.3047482694 -0.2069801581 -0.550875712
## [202,] -0.042662340 0.49913934 -0.5186429497 0.4553285736 -0.344718375
## [203,] -1.773111892 -0.17830822 -1.7400026462 1.2398085147 0.256196652
## [204,] 1.250439359 1.30927635 -1.2548155696 0.1212141597 1.352914243
## [205,] -1.763032603 -0.39026215 -1.0709293305 0.7285468245 -0.342694606
## [206,] -1.734908122 0.22532626 -1.3096386361 1.1382811564 -0.036594174
## [207,] -0.040455138 0.55449852 0.4573444687 -0.4218347821 -1.104169327
## [208,] -0.686284826 0.13219155 0.6118547014 -0.2432679726 -1.594675721
## [209,] -0.444359734 -0.28370817 -0.4495876614 -0.0769292704 -0.578337456
## [210,] 0.691490501 -1.91894081 -0.1931803231 -0.7485897999 -1.218968830
## [211,] 2.007551495 -1.38730232 -0.5519627527 -0.6174453995 -0.374722131
## [212,] 2.980951104 0.35496999 -1.5634230702 -0.6219160971 1.802482148
## [213,] -0.051043670 1.76211010 1.2088357396 -1.1338711513 -0.589252139
## [214,] -1.433696923 0.30117834 -1.1167790798 0.7158629306 0.010513237
## [215,] 0.663189426 0.17003794 -0.7914480913 0.1781148795 0.204851463
## [216,] 2.031410016 -1.22967790 -2.3061777513 2.1455817946 0.319442130
## [217,] 0.789603453 -0.46930287 -1.7356512834 -0.3692602528 1.111404116
## [218,] 0.673484381 -0.39280224 0.0473568504 1.1650225109 -1.817685120
## [219,] -1.540903396 -0.09859304 -1.1167612805 0.8029841934 -0.165862050
## [220,] 4.811125983 2.34468196 -0.3322754239 0.5855998508 1.125323479
## [221,] 2.960210184 0.25580109 -1.3532023514 1.1105279220 0.660503185
## [222,] 0.548555090 1.20673516 -0.5847280068 1.2403006951 -0.255814803
## [223,] -1.203818787 0.41491335 0.6516018979 -1.7888960008 -0.675920517
## [224,] -0.095903547 -0.65584776 -0.5358363119 -1.2541542670 0.075096599
## [225,] -1.447284264 -1.00724102 -0.6082703522 -1.5298781643 0.066886767
## [226,] -0.721456172 1.13787970 0.8467912909 -2.0802276689 -0.435596218
## [227,] 2.040310983 0.43242568 -0.2461052925 0.7423873284 -0.579002419
## [228,] 1.855207556 1.67633604 0.5148301396 -0.1260125667 -0.807029471
## [229,] -1.362709085 0.28203522 -1.2055884775 0.5729921576 0.186353531
## [230,] -0.288896751 0.20730044 0.2845176632 0.6308919312 -1.505210536
## [231,] -0.418601999 0.23532480 0.2238988269 -0.5027334058 -0.945826637
## [232,] -1.163850583 0.68497750 -0.8821849871 0.8863377110 0.002177941
## [233,] 0.411132602 1.16486925 -0.3493614654 1.3942763398 -0.698315265
## [234,] -1.693135796 -0.47771445 -1.0852001549 0.2466849979 -0.106371453
## [235,] -1.469262447 0.58168692 0.2179103849 0.0730339108 -1.083523772
## [236,] -1.241804213 1.79930936 0.0417415503 0.6900290082 -0.739436237
## [237,] 3.689808324 1.67054618 0.2271980354 -0.1712036874 0.320606604
## [238,] 0.637785394 -1.18641596 0.3164064662 0.3364686684 -2.013280789
## [239,] 6.741912903 1.29247340 -0.5420542885 0.4573219426 1.094774796
## [240,] -1.238593026 -0.23776840 -0.5949271348 -1.3969869040 0.325843132
## [241,] 0.823175506 1.06316740 -0.5254541417 -0.6645444043 0.438143394
## [242,] 0.046147404 1.10794300 0.9541899343 -1.0517974932 -1.112030077
## [243,] -0.926653518 -0.47703938 0.3584883210 0.7483755808 -2.030451588
## [244,] 1.642861658 0.76706108 0.4101327315 -1.6601340760 0.241603918
## [245,] 0.577872627 -0.27228218 0.0857683853 -1.3777634787 -0.319784341
## [246,] -1.754825326 0.80791517 0.5577871077 -0.0676093662 -1.377625236
## [247,] -2.038325012 0.13688760 -0.0003412363 0.3430358578 -1.217973430
## [248,] 0.534102452 0.42078510 -1.1547081981 -0.6235503927 0.941303310
## [249,] -0.778602587 0.16187841 -0.3007337578 -2.1397103069 0.556468021
## [250,] -1.358620602 -0.11871598 -0.0786250759 -1.0668656351 -0.441391917
## [251,] 0.552972231 -1.32892174 0.2653874378 -1.7448134449 -0.716425820
## [252,] 0.160512695 -1.07401603 -1.3645629081 0.1229912862 0.139386122
## [253,] -0.255760964 -1.55052571 -0.6215940219 -1.4389507212 -0.116189564
## [254,] 2.380048532 -1.22313608 -0.4828668231 -1.7734074221 0.293324720
## [255,] 2.562080786 -0.62564376 -0.7980444051 1.7530531164 -1.022362433
## [256,] -0.556325503 0.61870762 0.4208116759 0.5833612102 -1.567526425
## [257,] -1.361977024 0.48557037 -0.3780687286 -0.2263198361 -0.261824026
## [258,] -1.604168388 0.15729081 -1.1427967214 0.6878894786 -0.014904788
## [259,] 0.453544197 -0.10135935 -0.0830135546 -1.4480142567 -0.154195510
## [260,] -0.245088734 -0.21116664 -0.8071754259 0.2429511311 -0.279436645
## [261,] -0.586494355 0.59713665 -2.4100725243 -0.5973150226 2.411185160
## [262,] -0.595783004 -0.97017702 0.1712856607 -1.4091442191 -0.895962157
## [263,] -0.098509308 -0.71157736 -0.6190102919 -0.8101660640 -0.107118411
## [264,] -1.732739711 -0.01171917 -0.9714345094 0.9911466978 -0.385416176
## [265,] -1.312518153 2.21664937 1.0466799279 0.0855880150 -1.449625633
## [266,] -1.117483636 -1.07344208 -0.1309504223 0.5351107892 -1.625027906
## [267,] -0.802242010 2.43916871 -0.0658918448 0.5326247945 -0.249856505
## [268,] 1.779574174 -2.20525734 -1.2254437217 -1.4601618621 0.480018703
## [269,] -0.692885384 -0.50625416 -1.6109602188 1.2266062367 0.002189829
## [270,] -0.296827034 2.09903244 -0.5356781950 1.0212095064 0.236744458
## [271,] 2.648459041 -0.60314173 -1.1623236353 -1.1868983731 1.137440016
## [272,] -0.009329958 0.66837011 -0.6089249244 -0.0124265699 0.007020687
## [273,] 0.636626889 0.36453000 -1.0956031271 -0.4201642118 0.755836178
## [274,] -0.730329225 0.63180054 -0.2775908413 0.0076169716 -0.174167360
## [275,] 0.329127497 -0.70211196 -1.1270499206 -1.3794822582 0.788719121
## [276,] -1.859016837 -0.41444458 -1.0884680056 0.0004891493 0.032889030
## [277,] 2.011187895 -1.86028031 -1.4701740451 1.9592818340 -0.863881329
## [278,] 4.387657320 1.01990704 -1.0694317529 1.0313056985 0.910287718
## [279,] -1.562200265 0.50506920 0.3257902808 0.4071536855 -1.418071805
## [280,] 1.140064695 -0.84165314 0.0475366423 0.1828157194 -1.383731574
## [281,] -1.592089421 0.68980851 0.0241838972 -0.0763303675 -0.781020214
## [282,] -0.863852065 0.20642081 -0.8983962803 -1.0667886017 0.713765183
## [283,] 1.027169030 1.16456255 -1.0404846287 -0.0396471898 1.049317709
## [284,] -0.436517354 -0.42713213 0.0134409058 -0.8973018413 -0.722139204
## [285,] 0.337411799 -0.24417082 -0.6480989722 -0.0855047074 -0.227110796
## [286,] 0.922063650 -0.22614793 -1.9443047687 0.7895315305 1.017821370
## [287,] 0.074518204 0.02674638 -1.0857966267 0.5553685803 0.035340926
## [288,] 0.517903752 0.07720678 0.7802091323 -0.3889323964 -1.326401252
## [289,] 1.205633993 4.05992941 1.7774871852 0.5243784073 -0.779237256
## [290,] 5.667322803 1.41683162 0.5192606886 -0.5242010735 0.057913957
## [291,] 0.117634314 2.05280704 1.1202906141 -0.2225732744 -1.394044856
## [292,] -1.257776898 0.99085451 -0.6432249171 0.7239870280 -0.267413061
## [293,] -1.442594978 0.64860803 -1.1825132672 1.3464166771 -0.103965971
## [294,] 0.581815447 0.15948370 0.5111637426 -1.5852378542 -0.514462082
## [295,] 3.192976367 -0.80514579 0.6934590185 -0.6145019682 -1.279398203
## [296,] -1.664428065 0.44940153 -0.8138817842 0.9169350091 -0.409961580
## [297,] -1.381280799 -1.04718836 -0.8104653996 -1.2130194950 0.131190811
## [298,] -0.359580844 -0.02707621 -0.2139147820 0.7519546558 -1.081305483
## [299,] -1.295214100 0.90633579 0.3446284016 -0.9705650257 -0.587847432
## [300,] 1.275367360 -0.46955884 -0.9321790556 1.6880185073 -0.857351331
## [301,] 0.510190648 -0.47545309 0.1659852525 -1.4398287570 -0.586650046
## [302,] 0.497692443 0.73632621 -0.7320867366 -0.6396358886 0.543145415
## [303,] -0.360524908 1.94049135 -0.0814679929 -1.0578009624 0.492777950
## [304,] 0.680162177 4.39853961 1.3939873156 -0.0903894719 -0.359689359
## [305,] 0.651993920 1.46566547 -0.5054646735 1.4206026417 -0.393377040
## [306,] 3.788964776 -1.08829199 -1.2835697130 1.5189289232 -0.160003180
## [307,] 0.324102302 0.44636919 -0.0358560470 -1.7147746806 0.185602167
## [308,] 1.241627938 -0.80113200 -0.9370602561 0.5736384332 -0.380036721
## [309,] -0.511968929 -1.17458566 -0.6546640582 -0.3823368294 -0.528559592
## [310,] 0.718039754 0.17733890 -0.6884966946 -1.2988653722 0.666658316
## [311,] -0.310163020 -1.06311682 -0.8411613032 -0.3440185709 -0.239649145
## [312,] -1.033055205 1.28803157 -0.7885399882 1.0583019502 -0.014148637
## [313,] -0.764852259 0.84975776 -0.4166580478 -0.3570104900 0.163850456
## [314,] 2.840965510 1.27703956 1.2737033558 -0.0712572107 -1.299150219
## [315,] -1.178758036 -0.07789715 -0.1547232721 -1.1892312531 -0.258297637
## [316,] -0.802177079 -0.95036649 -0.6926590212 0.0641135168 -0.653215774
## [317,] 1.938258838 -1.28408318 -0.7550485265 -0.2456973992 -0.386044302
## [318,] -1.084340607 0.56509571 -0.3641566428 -0.4657496728 -0.069947785
## [319,] 5.007927517 1.33213703 0.4628978606 -0.6412930066 0.335503981
## [320,] -0.352175349 0.05184295 -1.0595996323 1.1419351290 -0.354514092
## [321,] -1.645893870 0.67772347 0.5678664419 -0.6516041624 -1.130232840
## [322,] -0.723629619 0.28418574 -0.9155428645 -1.7398043966 1.090294733
## [323,] 2.150497872 -1.85335253 -0.9536747162 -0.9930159522 0.090967074
## [324,] 0.219479185 0.70653560 0.4625353948 0.0635989317 -1.095438714
## [325,] -0.347437994 0.13601327 -0.3616040070 0.0995137840 -0.602584780
## [326,] -0.234908136 0.38370796 0.3810829977 0.2955102824 -1.313248723
## [327,] 0.016559745 -0.24813137 0.3418529439 -0.6289931873 -1.073354029
## [328,] -1.467247701 -0.93657939 -1.0073778050 -1.3484920808 0.464904725
## [329,] 1.154836707 -1.65839860 -0.1796696786 0.5786916927 -1.773817068
## [330,] 0.020892606 0.14389944 0.1408600742 0.1842691926 -0.953519579
## [331,] 0.169022729 0.24173475 0.6782816134 -1.3801420819 -0.971815989
## [332,] 0.596241854 0.70051500 -1.8052088015 -0.0053918173 1.465700551
## [333,] -1.658882001 -0.32657130 0.2318064743 -0.3636469103 -1.209182254
## [334,] -1.130296134 0.92484749 -0.3380519552 -0.3013039197 -0.112208131
## [335,] -0.114349001 -0.27920208 -0.6403335111 -0.2074405468 -0.257747260
## [336,] -1.180178802 0.03183833 -0.3500656477 -1.0972084429 -0.005358715
## [337,] 1.016962553 -1.84125842 -1.0359966156 0.1725787385 -0.567197423
## [338,] 1.874901202 -1.13532877 -0.6093993174 1.0930613053 -1.160229327
## [339,] -1.674481841 0.44986836 2.1646104925 0.9678148811 0.135461099
## [340,] 0.347838749 -0.88857174 0.8771393702 -0.0399280185 1.772672225
## [341,] -0.523787799 -0.92658682 1.5418929659 0.1325485002 0.785980424
## [342,] -1.191298001 1.23405600 1.7890495622 1.3692564275 0.892653715
## [343,] 1.808772263 -1.69685692 0.8907964331 -0.2029722962 1.489618576
## [344,] -1.770065768 -0.81617964 1.3539885104 -0.2766980579 1.166492368
## [345,] -0.206433118 0.56197089 1.8053747930 1.3814075643 0.495893161
## [346,] 0.781356058 -0.26730308 1.4981375832 0.8043655618 1.134248369
## [347,] -1.821829245 -1.41978625 1.5929954355 -0.6929508188 0.865846962
## [348,] -0.284787326 -0.98055909 2.0711730642 -0.3625595662 0.392274537
## [349,] -0.436832085 1.81979653 1.9654352950 0.0409412675 1.657960929
## [350,] -1.217940564 -0.03242505 1.5341269350 0.0689673368 1.157904466
## [351,] 1.408443279 -0.92755403 2.5527909101 -0.6932672647 0.150225917
## [352,] 0.076806137 -0.36230781 1.0569801425 0.7081503355 1.356282603
## [353,] -1.371613972 -0.73826316 -0.0390647200 0.5827617423 2.417181597
## [354,] -1.864312777 -1.17836386 1.6190160585 -0.8239266507 0.990897877
## [355,] -1.989259900 -1.78295952 1.5112558257 -0.6883823148 0.805384073
## [356,] -0.666931670 0.04442279 0.9603229118 1.9679277491 0.821582895
## [357,] -0.752021652 0.57932223 1.1919215542 0.0297044937 1.852331941
## [358,] -0.799705965 -1.07103612 0.3748144882 2.1390626788 1.010092176
## [359,] -1.601727166 -1.41026284 0.7915067164 -0.2584759327 1.601877583
## [360,] -1.657122757 0.50517962 1.7207936026 1.3778309508 0.405279647
## [361,] -0.384493964 -0.88081329 0.5179378168 0.9525680456 1.560400572
## [362,] -1.117824446 0.07013439 2.3329630062 -0.8981794794 0.738754653
## [363,] 2.156938592 -0.59054334 0.9679981313 1.4564801625 1.063503699
## [364,] -0.789754021 -2.12761614 1.4729430325 0.0219314842 0.410727684
## [365,] -1.380570918 -1.02926654 1.9974600705 -1.3875631548 0.968366183
## [366,] -1.291560292 0.38334086 1.4160677141 1.5258026469 0.762317564
## [367,] -0.935262338 0.56231264 2.1242791830 0.3720182728 0.718006182
## [368,] 2.492171120 -0.48928746 2.4676282836 1.9668068431 -0.727490529
## [369,] -0.327363502 -0.84626614 2.2688783371 0.9603180211 -0.407816836
## [370,] -1.468296601 0.18028669 1.6652393313 1.5773153771 0.412661443
## [371,] 0.644477407 1.35334644 2.6883609615 0.5712489712 0.440528158
## [372,] 4.369563022 -1.66481832 1.6865361527 0.4901972904 0.760040778
## [373,] -2.357052820 -1.26900605 1.5231357317 1.0301102498 0.074632682
## [374,] 0.718708019 0.22127710 1.0354060443 0.2583339391 1.891779073
## [375,] 1.391878059 0.98004221 1.7111474295 -0.7952838709 2.265775349
## [376,] 0.905097897 -0.22694710 2.1140189340 0.5476029310 0.603860387
## [377,] 3.157230391 -1.19754195 1.1484347290 1.0599855046 1.186962665
## [378,] 0.003135705 -0.90598915 1.6393299343 -1.1011824448 1.359035590
## [379,] -0.242056357 -0.73255189 1.7021620290 -0.1866470103 0.800865246
## PC6 PC7
## [1,] 0.814428206 -0.107883916
## [2,] -0.048912344 -0.099604504
## [3,] -0.086507916 -0.138527863
## [4,] -0.822748232 0.360506834
## [5,] -0.108812986 0.078970882
## [6,] 0.183797925 0.433343571
## [7,] 0.008911379 -0.004657966
## [8,] 0.543125568 -0.332707934
## [9,] -0.752701863 0.056474342
## [10,] -0.441826427 -1.924448799
## [11,] -0.244944687 0.159851097
## [12,] 0.206259597 -0.169273224
## [13,] 0.163519054 -0.103667561
## [14,] 0.132474346 0.108653816
## [15,] -1.324055932 -0.183915616
## [16,] 0.714919089 0.304537991
## [17,] -0.647376538 0.365592105
## [18,] 1.097596271 -0.377715183
## [19,] 0.334391075 -0.234827285
## [20,] 0.808587321 -0.200036177
## [21,] 0.322170368 -0.166529357
## [22,] 0.107803508 0.012805983
## [23,] -0.332323319 -0.202474142
## [24,] 0.995998868 0.201016672
## [25,] -2.363493528 0.266625584
## [26,] -0.813907073 -0.571488560
## [27,] -2.160783056 0.281527887
## [28,] 0.098479393 0.336756957
## [29,] 0.004273460 -0.381406184
## [30,] -0.044211599 -0.418300721
## [31,] -0.128464996 0.054899611
## [32,] -0.357344175 0.183909490
## [33,] -0.597244606 0.289672968
## [34,] 0.259235600 0.349194654
## [35,] -0.236888897 -0.371166651
## [36,] -0.249251785 0.050335461
## [37,] 0.607590347 -0.462113845
## [38,] -0.026797156 0.355817879
## [39,] 0.166045669 -0.073826942
## [40,] -0.162738506 -0.392300116
## [41,] -0.522507663 -0.121724380
## [42,] 0.067225848 0.209115377
## [43,] -0.417780877 -0.474060203
## [44,] -0.173878940 -0.457967209
## [45,] -0.050403121 -0.134114068
## [46,] -0.089979747 -0.491479393
## [47,] 0.480573605 -0.072323181
## [48,] 0.228887831 0.155522234
## [49,] -0.489991807 -0.227097997
## [50,] -0.606582969 -0.101166456
## [51,] 0.577660866 -0.455756839
## [52,] 0.585446120 -0.388137976
## [53,] 0.734811073 1.561539615
## [54,] 1.381511548 0.252947237
## [55,] 0.358959045 -0.182311216
## [56,] 0.207910788 0.078632864
## [57,] 0.607774154 -0.281869942
## [58,] 2.443161543 0.443513680
## [59,] 0.206843192 0.253038172
## [60,] 0.135499206 0.164773439
## [61,] 0.648725932 0.351461678
## [62,] 0.166486526 0.246682271
## [63,] -0.513948300 -0.286040883
## [64,] 1.163578265 0.263125274
## [65,] -0.009862807 0.134046265
## [66,] -0.730377136 0.337181681
## [67,] -1.487448857 -0.149925371
## [68,] 0.220853759 0.272493773
## [69,] -0.588054260 0.260689981
## [70,] -0.385273067 0.319508713
## [71,] -0.175254751 1.897246402
## [72,] -1.300330063 -0.404208363
## [73,] 0.816322549 -0.225387244
## [74,] -0.060212427 0.165026305
## [75,] -1.649589162 -0.529795744
## [76,] 0.569158827 -0.263377372
## [77,] -0.165692949 -0.401192949
## [78,] 0.043436354 0.440699177
## [79,] 0.327782857 0.371732847
## [80,] 0.016945132 0.140928440
## [81,] -0.877693420 -0.271276638
## [82,] 0.050656761 0.314869348
## [83,] 0.024270266 -0.489647178
## [84,] -0.428408376 0.144447332
## [85,] 0.302353058 0.176709283
## [86,] -0.930367776 -0.038966156
## [87,] 0.206974359 1.518547012
## [88,] 0.773220076 0.387655208
## [89,] -0.057425863 0.311702214
## [90,] -0.319492539 -0.104439493
## [91,] 0.464021241 -0.182053564
## [92,] 0.568469956 0.135273025
## [93,] -0.637098352 -0.352179961
## [94,] -0.897710356 -0.603436508
## [95,] -0.302718373 0.134220300
## [96,] 0.796303291 -0.453234619
## [97,] 0.102248374 -0.373850042
## [98,] 0.276775028 -0.386841666
## [99,] -0.147547074 -2.150145655
## [100,] 0.522935395 -0.336156710
## [101,] -1.015284422 -0.131608533
## [102,] 0.945355253 0.288290374
## [103,] 0.240503118 0.089283023
## [104,] 0.040655927 -0.326527188
## [105,] 0.156719385 -0.425753859
## [106,] -0.378077108 -0.375663969
## [107,] 0.617517671 -0.018331347
## [108,] -0.140360458 0.357139007
## [109,] -0.369058053 -0.363453154
## [110,] 1.367651547 -0.052494633
## [111,] -0.245674045 0.171961839
## [112,] -0.288279169 -0.437854120
## [113,] 0.654181743 0.335734007
## [114,] 0.430171258 0.242838061
## [115,] -0.609725681 -0.399796060
## [116,] -0.153071461 0.293451739
## [117,] 0.435961104 0.348338090
## [118,] -1.122876095 0.371334968
## [119,] 0.128953459 -0.002950892
## [120,] 0.454338848 -0.320002000
## [121,] -0.393321862 0.002244332
## [122,] 0.694427666 -1.776651924
## [123,] -1.480360092 0.237363812
## [124,] 0.563305776 0.061168635
## [125,] 0.789672355 0.182676841
## [126,] 0.657430786 0.151394277
## [127,] 0.052053042 -0.260063201
## [128,] -0.509971776 0.300299579
## [129,] -0.514688913 0.253498821
## [130,] -0.230653718 0.334001823
## [131,] 0.234492897 0.070164155
## [132,] -0.509623760 0.211476411
## [133,] -0.508032972 0.218820879
## [134,] -0.584676128 0.432040803
## [135,] -0.599512631 0.114578050
## [136,] 0.742555446 0.264941606
## [137,] 0.215593238 -0.296341138
## [138,] 0.814373445 -0.463329220
## [139,] -0.705236433 0.235224585
## [140,] -0.240819937 0.128832004
## [141,] -0.738265473 0.045748305
## [142,] -0.516065685 0.423763629
## [143,] 1.032627703 0.255695270
## [144,] 1.011640901 -0.046612704
## [145,] 1.036057364 -0.116502648
## [146,] 0.238779557 -0.094409829
## [147,] 0.093045275 -0.025943269
## [148,] -0.018285774 0.063985702
## [149,] -0.821062597 0.316957388
## [150,] -0.051433159 -0.325889337
## [151,] 0.240258258 0.157499206
## [152,] 0.244055313 -0.484326189
## [153,] 0.321762278 0.347844280
## [154,] -0.688031620 0.275674116
## [155,] 0.052870105 0.278750325
## [156,] 0.259394959 0.994613529
## [157,] 0.384573263 0.255112420
## [158,] -0.647167228 0.095523521
## [159,] -0.447355557 -0.367626528
## [160,] -1.037268876 -0.081314104
## [161,] 0.685349399 -0.373379228
## [162,] -0.574402441 -0.041182433
## [163,] -0.812645636 0.354791023
## [164,] 0.259528832 0.196856471
## [165,] -0.112837907 -0.422270866
## [166,] 0.128000241 -0.175939627
## [167,] -0.895512404 0.337192272
## [168,] -0.711019273 -0.814804273
## [169,] 0.218357219 -0.033915231
## [170,] -0.078144315 0.263676922
## [171,] 0.789052948 0.069697557
## [172,] 0.334044498 0.095799549
## [173,] -0.466799910 0.182242801
## [174,] -0.409218588 0.105315011
## [175,] 0.475675622 0.157100174
## [176,] 0.631970192 -0.312887516
## [177,] -0.842796008 0.184336624
## [178,] -0.521271064 0.253595738
## [179,] -0.195535437 -0.489681481
## [180,] -0.238968439 0.339455192
## [181,] 1.224469205 0.162311433
## [182,] 0.896759582 -0.187133556
## [183,] -0.369525579 0.051355060
## [184,] -1.133798661 -0.032484936
## [185,] -0.525703790 0.938668397
## [186,] 0.115704613 -0.308573611
## [187,] -0.330011041 0.052298230
## [188,] 0.252831722 -0.344500770
## [189,] 0.478267892 -0.411989559
## [190,] 0.108389410 0.270176494
## [191,] 0.320051815 -0.452948617
## [192,] -0.927317654 0.050049377
## [193,] 0.049967323 0.232020283
## [194,] -0.322439393 -0.332013839
## [195,] -0.576452643 0.112196595
## [196,] -0.426323754 0.064708147
## [197,] 0.577314293 -0.090994712
## [198,] -0.220002645 -0.145293651
## [199,] 1.007924154 -0.238873759
## [200,] -0.144916255 -0.256657796
## [201,] 0.222523935 -0.327353336
## [202,] 0.143637470 -0.384469784
## [203,] -0.685873899 0.077706170
## [204,] -0.684433914 -0.555287379
## [205,] -0.739601209 0.286336764
## [206,] -0.391145161 0.071275723
## [207,] 1.031184262 -0.071523474
## [208,] 0.422795216 -0.361912372
## [209,] 0.232252275 -0.321891385
## [210,] 0.132512399 -2.194006418
## [211,] 0.300407101 0.236278993
## [212,] -0.181056517 -0.655811887
## [213,] -2.264161275 0.013076856
## [214,] -0.146543860 0.258375350
## [215,] -0.914443039 -0.156858207
## [216,] 0.163052914 0.373094641
## [217,] 0.735902331 0.298434341
## [218,] 0.858016687 -0.410620478
## [219,] -0.698483214 0.291328307
## [220,] -1.702108557 -0.103054608
## [221,] -0.570947694 -0.064210529
## [222,] 0.103014117 -0.154551366
## [223,] 0.032313480 0.248280548
## [224,] -0.245512705 -0.395034205
## [225,] -0.795643311 0.316447811
## [226,] 0.757677018 0.355289619
## [227,] 0.112343498 -0.370694673
## [228,] 2.840081863 -0.472760040
## [229,] -0.117535015 0.251369052
## [230,] -0.123999729 -0.103219333
## [231,] 0.620151206 -0.398726087
## [232,] -1.258499518 0.031686285
## [233,] 0.508788077 0.031702502
## [234,] -0.730990134 0.229897436
## [235,] -0.131943879 0.351750927
## [236,] 0.930178961 0.218030323
## [237,] -1.155883577 -0.406938969
## [238,] 0.421016873 -0.245001577
## [239,] -0.919968833 0.339656927
## [240,] -0.475488496 0.136247856
## [241,] 1.761754259 0.029538972
## [242,] 1.222218060 -0.319429458
## [243,] -0.387563364 -0.168870331
## [244,] -1.348003518 -0.078702906
## [245,] -0.096908019 0.116533237
## [246,] 0.123274608 0.151123503
## [247,] -0.489960306 0.098338159
## [248,] 0.676566199 -0.339944716
## [249,] 0.072286130 0.262572292
## [250,] -0.203974262 0.359934672
## [251,] -0.962511140 0.447744836
## [252,] 0.026617023 0.293556296
## [253,] -0.615601226 -0.158798853
## [254,] 0.165313198 0.013008846
## [255,] 1.432136191 1.223639292
## [256,] 0.483977624 -0.346520349
## [257,] -0.153805545 0.159416002
## [258,] -0.327177547 0.145372443
## [259,] 0.927279628 0.136024542
## [260,] 0.347645497 -0.209884830
## [261,] 0.229700925 -0.104543344
## [262,] -0.158104523 -0.333049945
## [263,] -0.057284357 -0.187261115
## [264,] -1.002026891 0.117204649
## [265,] 1.233710972 0.172803485
## [266,] -0.621049559 -0.266818669
## [267,] 1.556396291 0.244375096
## [268,] -0.067622566 -0.072725103
## [269,] -0.175077307 -0.498801012
## [270,] -0.666813685 0.155867363
## [271,] -0.136040334 -0.327359471
## [272,] 0.778990215 -0.465309183
## [273,] 0.693723928 -0.130197667
## [274,] -1.468695169 0.266972231
## [275,] 0.429361577 -0.105547847
## [276,] -0.773390730 -0.033260132
## [277,] 0.336674762 1.064820895
## [278,] -0.300804152 0.703841870
## [279,] -0.238262975 0.450690335
## [280,] 0.395969716 -0.242043012
## [281,] 0.109021256 0.138748544
## [282,] -0.037963898 0.268885486
## [283,] -0.373873694 -0.512209208
## [284,] -0.029714459 -0.403875221
## [285,] 0.426625104 0.228719436
## [286,] -0.362288537 0.223311049
## [287,] 0.384277844 -0.106878993
## [288,] -1.421668738 0.046595855
## [289,] -2.984199195 0.075859453
## [290,] 1.319916883 2.001667923
## [291,] 2.046793198 -0.269649215
## [292,] 0.392813424 0.303644436
## [293,] 0.021688217 0.270137554
## [294,] -0.049144987 -0.046060227
## [295,] -1.011855498 -0.955345258
## [296,] -0.175912153 0.163389864
## [297,] -0.811118093 0.416648260
## [298,] -0.340865035 -0.224224889
## [299,] 0.466059600 0.157785884
## [300,] 0.558304051 -0.192471657
## [301,] 0.750653613 0.459663166
## [302,] 1.122352945 -0.276052847
## [303,] 1.078964668 0.210264826
## [304,] 0.426300512 0.141513828
## [305,] 0.810547774 0.065859782
## [306,] -0.181814543 1.697357273
## [307,] 0.699571022 -0.449062901
## [308,] 0.145047367 -0.510569761
## [309,] -0.335948519 -0.163889426
## [310,] 0.695110312 -0.089730044
## [311,] -0.421019920 -0.164631917
## [312,] -0.328893323 0.125575320
## [313,] -0.600269847 0.190331629
## [314,] -0.800239413 -0.264240505
## [315,] -0.079057717 0.438769076
## [316,] -0.386407008 -0.406110560
## [317,] 1.041640267 0.390303651
## [318,] -0.189857024 0.234508553
## [319,] -1.090183460 0.762300322
## [320,] 0.386282802 -0.239807387
## [321,] 0.134404520 0.127105246
## [322,] 0.366835108 0.216268360
## [323,] 0.342909111 0.372677157
## [324,] -0.254516438 -0.193658003
## [325,] 0.533845103 -0.328861238
## [326,] -0.465612342 -0.352871158
## [327,] -0.163023346 0.003333250
## [328,] -0.798713796 0.164392019
## [329,] 0.481838526 -1.448359073
## [330,] -1.226111979 -0.366016068
## [331,] 1.020308661 0.044230674
## [332,] 1.056394345 -0.394589336
## [333,] -1.007313550 0.374213944
## [334,] 0.492601789 0.244276984
## [335,] 0.411613111 -0.135788109
## [336,] -0.280767946 0.263720304
## [337,] 0.160862506 -0.192753984
## [338,] 0.791036742 0.678047807
## [339,] 0.126529280 0.120748763
## [340,] 0.262317102 -0.088849352
## [341,] 0.041119374 -0.483927739
## [342,] -0.678266870 -0.258446039
## [343,] 1.445310485 0.036985630
## [344,] -0.175915279 0.027902348
## [345,] 0.564004554 -0.503273137
## [346,] -1.123890798 -0.049820336
## [347,] -0.529962184 0.213624141
## [348,] 0.448319463 -0.109057231
## [349,] 0.164185074 -0.178027089
## [350,] 0.343302649 0.295711308
## [351,] 1.064600476 -0.399557062
## [352,] 0.402428026 -0.264910522
## [353,] -0.039235833 0.080955691
## [354,] -0.401278508 0.033682397
## [355,] -0.845062983 0.190359077
## [356,] 0.916027349 -0.545821754
## [357,] 0.946629462 0.303161216
## [358,] -0.119192699 -0.421977595
## [359,] -0.474603729 0.232244290
## [360,] 0.620269650 0.217072532
## [361,] 0.290272477 -0.446292100
## [362,] 0.807055770 0.427223893
## [363,] 1.725250067 0.275888197
## [364,] -0.573212533 -0.177662617
## [365,] -0.242829260 0.310782840
## [366,] -0.025556816 0.310309937
## [367,] -0.369535370 0.246732337
## [368,] 0.794924538 0.929445109
## [369,] -0.044906053 0.144701045
## [370,] -0.730353345 0.202922032
## [371,] 0.105639703 -0.429239913
## [372,] -0.245135971 0.186120856
## [373,] -0.823120736 0.174853047
## [374,] 1.126518713 -0.084801083
## [375,] -0.200011773 -0.549385252
## [376,] -1.229143214 0.135743929
## [377,] -0.299503313 0.743333133
## [378,] 0.410392839 -0.361555114
## [379,] 0.837670932 -0.196874004
plot(Cancer_pca)
#get the original value of the data based on PCA
center <- Cancer_pca$center
scale <- Cancer_pca$scale
new_Cancer <- as.matrix(Cancer[,-1])
new_Cancer
## Age Stage Tumor Size Regional Node Examined Reginol Node Positive
## [1,] 68 1 4 24 1
## [2,] 50 2 35 14 5
## [3,] 58 3 63 14 7
## [4,] 58 1 18 2 1
## [5,] 47 2 41 3 1
## [6,] 51 1 20 18 2
## [7,] 51 1 8 11 1
## [8,] 40 2 30 9 1
## [9,] 40 4 103 20 18
## [10,] 69 4 32 21 12
## [11,] 68 1 13 9 1
## [12,] 46 3 59 11 3
## [13,] 65 2 35 13 3
## [14,] 48 1 15 23 7
## [15,] 62 2 35 16 14
## [16,] 61 1 19 20 1
## [17,] 56 2 46 1 1
## [18,] 43 2 24 22 1
## [19,] 48 2 25 16 1
## [20,] 60 2 29 20 1
## [21,] 48 2 30 15 2
## [22,] 57 2 40 15 5
## [23,] 55 2 29 4 1
## [24,] 48 3 70 18 1
## [25,] 62 1 20 26 22
## [26,] 63 2 22 31 17
## [27,] 48 2 50 25 23
## [28,] 46 1 17 14 1
## [29,] 57 2 25 14 4
## [30,] 66 2 21 10 1
## [31,] 47 2 40 3 1
## [32,] 53 1 15 5 1
## [33,] 59 1 15 6 1
## [34,] 60 1 20 19 3
## [35,] 46 2 30 19 10
## [36,] 51 1 10 9 2
## [37,] 54 2 27 21 6
## [38,] 51 1 18 14 2
## [39,] 49 2 35 10 2
## [40,] 51 2 23 15 5
## [41,] 57 3 70 12 12
## [42,] 64 1 17 12 2
## [43,] 62 2 21 2 1
## [44,] 53 2 23 15 6
## [45,] 55 1 5 11 2
## [46,] 66 3 51 10 5
## [47,] 42 1 9 15 2
## [48,] 62 1 15 12 1
## [49,] 53 2 32 16 9
## [50,] 69 1 5 8 3
## [51,] 37 2 23 17 3
## [52,] 69 3 55 9 1
## [53,] 60 3 120 7 1
## [54,] 63 3 77 20 2
## [55,] 57 1 2 16 1
## [56,] 55 1 11 13 1
## [57,] 62 2 25 19 1
## [58,] 50 1 18 49 1
## [59,] 50 1 15 15 1
## [60,] 55 1 12 17 2
## [61,] 56 1 18 24 2
## [62,] 51 1 17 12 1
## [63,] 42 2 26 1 1
## [64,] 59 3 75 20 2
## [65,] 67 1 13 16 3
## [66,] 46 1 15 5 1
## [67,] 31 3 70 23 23
## [68,] 40 1 15 20 3
## [69,] 58 1 15 5 1
## [70,] 52 1 17 12 3
## [71,] 49 3 130 12 8
## [72,] 64 2 34 24 20
## [73,] 31 2 30 16 1
## [74,] 66 1 10 15 1
## [75,] 67 2 22 19 16
## [76,] 56 3 55 13 1
## [77,] 66 2 25 11 4
## [78,] 42 2 50 7 1
## [79,] 51 2 50 9 1
## [80,] 68 1 15 9 1
## [81,] 53 2 30 21 13
## [82,] 67 1 20 10 1
## [83,] 66 2 22 9 2
## [84,] 53 1 15 2 1
## [85,] 51 1 15 13 1
## [86,] 46 2 40 12 11
## [87,] 48 3 120 7 5
## [88,] 52 3 80 10 1
## [89,] 55 1 17 11 1
## [90,] 65 1 3 9 1
## [91,] 53 3 60 8 1
## [92,] 33 1 14 15 1
## [93,] 63 2 26 5 4
## [94,] 45 2 25 21 16
## [95,] 59 1 12 12 3
## [96,] 60 2 25 17 2
## [97,] 50 2 30 4 2
## [98,] 61 2 25 10 1
## [99,] 50 4 24 3 3
## [100,] 68 2 27 14 1
## [101,] 38 3 70 33 24
## [102,] 47 1 16 25 1
## [103,] 39 2 45 3 1
## [104,] 57 2 27 7 1
## [105,] 52 2 23 14 3
## [106,] 60 2 25 2 1
## [107,] 54 2 40 11 1
## [108,] 68 1 20 12 2
## [109,] 38 2 21 8 2
## [110,] 63 2 36 30 3
## [111,] 61 1 14 15 4
## [112,] 37 3 51 3 3
## [113,] 46 2 50 34 10
## [114,] 45 2 45 14 2
## [115,] 54 3 51 6 5
## [116,] 53 1 19 12 3
## [117,] 50 3 76 9 1
## [118,] 69 1 20 16 9
## [119,] 48 2 35 15 3
## [120,] 53 2 27 15 2
## [121,] 67 2 35 7 2
## [122,] 43 4 35 15 3
## [123,] 50 2 50 16 16
## [124,] 59 2 38 23 4
## [125,] 53 1 15 23 2
## [126,] 62 1 17 16 1
## [127,] 39 2 25 13 2
## [128,] 59 1 19 3 1
## [129,] 56 1 15 8 2
## [130,] 45 1 18 13 3
## [131,] 60 1 11 14 1
## [132,] 50 2 45 10 6
## [133,] 58 1 12 8 1
## [134,] 50 1 20 5 1
## [135,] 55 2 45 8 7
## [136,] 37 1 18 28 5
## [137,] 46 2 25 12 1
## [138,] 65 2 21 20 1
## [139,] 61 2 49 14 10
## [140,] 52 3 70 18 9
## [141,] 54 1 7 4 1
## [142,] 36 1 19 13 4
## [143,] 49 1 17 24 1
## [144,] 62 2 38 23 3
## [145,] 54 2 34 20 1
## [146,] 61 2 30 15 1
## [147,] 46 1 4 18 2
## [148,] 38 3 72 13 8
## [149,] 66 1 18 1 1
## [150,] 59 2 25 13 3
## [151,] 38 1 9 18 1
## [152,] 67 2 21 14 2
## [153,] 60 1 20 15 1
## [154,] 61 1 15 14 5
## [155,] 67 1 18 14 2
## [156,] 69 3 100 16 6
## [157,] 47 1 17 15 1
## [158,] 39 1 7 6 1
## [159,] 53 2 24 2 1
## [160,] 55 2 43 14 14
## [161,] 59 2 30 18 4
## [162,] 53 1 7 3 1
## [163,] 59 1 18 2 1
## [164,] 57 1 12 20 2
## [165,] 61 2 25 16 6
## [166,] 68 3 62 3 1
## [167,] 54 1 20 12 7
## [168,] 37 4 70 24 17
## [169,] 48 2 37 8 1
## [170,] 53 1 13 14 1
## [171,] 69 2 40 20 2
## [172,] 63 3 70 11 3
## [173,] 49 1 12 9 2
## [174,] 63 1 9 9 1
## [175,] 60 1 10 24 2
## [176,] 41 3 55 11 1
## [177,] 59 1 18 17 10
## [178,] 43 1 15 7 2
## [179,] 52 2 25 31 14
## [180,] 61 2 50 11 5
## [181,] 60 1 10 32 1
## [182,] 61 2 30 23 2
## [183,] 63 1 13 3 1
## [184,] 48 2 40 15 13
## [185,] 51 3 100 14 11
## [186,] 66 2 25 14 2
## [187,] 68 3 68 3 3
## [188,] 58 2 25 14 2
## [189,] 62 2 23 34 9
## [190,] 46 1 15 14 1
## [191,] 58 2 22 12 1
## [192,] 60 1 7 2 1
## [193,] 62 1 16 19 4
## [194,] 53 2 24 5 1
## [195,] 42 3 75 16 13
## [196,] 63 1 11 5 1
## [197,] 55 2 35 16 2
## [198,] 50 3 60 10 5
## [199,] 52 2 30 22 2
## [200,] 47 2 25 11 2
## [201,] 55 2 25 14 2
## [202,] 60 2 25 16 4
## [203,] 66 1 12 1 1
## [204,] 50 2 25 17 12
## [205,] 64 1 17 2 1
## [206,] 67 1 11 6 1
## [207,] 56 2 32 24 1
## [208,] 60 2 21 18 1
## [209,] 56 2 25 12 1
## [210,] 48 4 19 6 1
## [211,] 44 3 75 11 4
## [212,] 37 3 52 17 12
## [213,] 52 1 9 18 17
## [214,] 63 1 17 9 1
## [215,] 54 2 35 10 9
## [216,] 63 3 85 4 4
## [217,] 44 2 50 12 1
## [218,] 68 3 51 17 1
## [219,] 64 1 18 4 2
## [220,] 50 3 75 27 27
## [221,] 55 3 72 14 13
## [222,] 66 2 35 20 7
## [223,] 46 1 12 18 2
## [224,] 43 2 23 9 3
## [225,] 43 1 16 2 1
## [226,] 43 1 16 27 2
## [227,] 59 3 57 20 9
## [228,] 55 3 50 42 1
## [229,] 61 1 17 9 1
## [230,] 66 2 32 15 4
## [231,] 55 2 21 19 1
## [232,] 65 1 11 7 7
## [233,] 69 2 40 22 5
## [234,] 59 1 15 2 1
## [235,] 63 1 17 15 2
## [236,] 68 1 14 26 1
## [237,] 48 3 60 26 21
## [238,] 61 3 55 12 1
## [239,] 43 4 120 28 26
## [240,] 44 1 11 8 2
## [241,] 47 2 39 29 1
## [242,] 52 2 23 30 2
## [243,] 69 2 28 9 2
## [244,] 39 2 37 18 15
## [245,] 43 2 40 15 5
## [246,] 64 1 9 18 1
## [247,] 66 1 8 9 1
## [248,] 45 2 28 18 3
## [249,] 37 1 15 15 2
## [250,] 50 1 17 11 1
## [251,] 40 2 50 6 6
## [252,] 52 2 48 5 1
## [253,] 41 2 30 2 2
## [254,] 32 3 68 13 6
## [255,] 65 3 110 19 2
## [256,] 67 2 23 20 2
## [257,] 57 1 12 13 2
## [258,] 63 1 13 7 1
## [259,] 42 2 40 20 1
## [260,] 57 2 30 12 1
## [261,] 42 1 9 11 2
## [262,] 46 2 22 9 1
## [263,] 47 2 30 9 2
## [264,] 67 1 12 3 3
## [265,] 67 1 10 33 1
## [266,] 65 2 25 3 1
## [267,] 65 1 16 33 1
## [268,] 33 3 65 3 3
## [269,] 64 2 22 4 1
## [270,] 66 1 17 20 10
## [271,] 34 3 60 13 9
## [272,] 55 2 22 20 2
## [273,] 47 2 35 18 3
## [274,] 58 1 18 9 9
## [275,] 38 2 34 11 1
## [276,] 57 1 6 2 1
## [277,] 65 3 105 4 2
## [278,] 52 3 100 23 17
## [279,] 67 1 20 14 2
## [280,] 57 3 57 14 3
## [281,] 61 1 10 16 1
## [282,] 45 1 17 12 2
## [283,] 50 2 25 18 10
## [284,] 50 2 21 12 2
## [285,] 53 2 45 14 2
## [286,] 54 2 50 7 6
## [287,] 58 2 35 13 2
## [288,] 56 2 38 12 11
## [289,] 68 1 16 30 28
## [290,] 41 3 140 41 15
## [291,] 61 2 25 39 1
## [292,] 65 1 18 17 1
## [293,] 69 1 18 11 1
## [294,] 43 2 34 19 6
## [295,] 47 4 65 14 14
## [296,] 67 1 13 10 1
## [297,] 45 1 20 1 1
## [298,] 65 2 29 11 4
## [299,] 53 1 10 21 1
## [300,] 67 3 62 13 3
## [301,] 43 2 50 18 1
## [302,] 47 2 29 23 2
## [303,] 48 1 15 30 3
## [304,] 62 1 15 46 14
## [305,] 68 2 42 25 5
## [306,] 57 3 130 10 10
## [307,] 40 2 21 22 3
## [308,] 56 3 51 10 4
## [309,] 52 2 30 4 1
## [310,] 40 2 35 19 3
## [311,] 51 2 31 4 2
## [312,] 67 1 14 15 5
## [313,] 54 1 15 14 6
## [314,] 56 3 60 27 17
## [315,] 48 1 20 12 1
## [316,] 57 2 22 4 1
## [317,] 47 3 80 14 1
## [318,] 54 1 15 14 3
## [319,] 41 3 100 28 23
## [320,] 65 2 30 12 1
## [321,] 58 1 8 18 1
## [322,] 38 1 15 15 1
## [323,] 38 3 80 8 3
## [324,] 60 2 30 19 7
## [325,] 58 2 25 16 1
## [326,] 63 2 24 15 6
## [327,] 53 2 35 14 4
## [328,] 43 1 12 1 1
## [329,] 60 4 45 9 1
## [330,] 60 2 25 10 9
## [331,] 47 2 35 24 1
## [332,] 48 2 28 19 2
## [333,] 59 1 17 6 3
## [334,] 56 1 15 19 1
## [335,] 53 2 32 13 1
## [336,] 48 1 15 11 2
## [337,] 52 3 60 4 1
## [338,] 61 3 90 13 2
## [339,] 66 1 11 19 3
## [340,] 45 2 37 13 4
## [341,] 52 2 21 12 3
## [342,] 67 1 2 19 9
## [343,] 40 3 70 17 1
## [344,] 50 1 8 9 1
## [345,] 65 2 22 23 5
## [346,] 55 2 40 12 12
## [347,] 47 1 13 5 1
## [348,] 49 2 32 16 2
## [349,] 53 1 5 29 9
## [350,] 53 1 18 17 2
## [351,] 44 3 52 24 4
## [352,] 54 2 31 16 4
## [353,] 51 1 14 6 1
## [354,] 46 1 7 7 1
## [355,] 47 1 12 1 1
## [356,] 68 2 21 18 1
## [357,] 50 1 20 23 2
## [358,] 67 2 26 5 2
## [359,] 47 1 16 3 1
## [360,] 68 1 15 20 1
## [361,] 55 2 25 10 2
## [362,] 47 1 20 23 1
## [363,] 56 3 80 24 3
## [364,] 51 2 30 2 2
## [365,] 41 1 16 11 2
## [366,] 67 1 20 16 4
## [367,] 58 1 17 19 7
## [368,] 67 3 100 25 8
## [369,] 63 2 41 14 4
## [370,] 69 1 16 12 6
## [371,] 59 2 25 30 11
## [372,] 44 4 108 16 14
## [373,] 65 1 12 2 1
## [374,] 48 2 38 24 4
## [375,] 39 2 24 26 13
## [376,] 55 2 45 14 13
## [377,] 50 3 98 14 12
## [378,] 39 2 25 16 3
## [379,] 49 2 30 18 1
## Survival Months Sex
## [1,] 60 0
## [2,] 62 0
## [3,] 75 0
## [4,] 84 0
## [5,] 50 0
## [6,] 89 0
## [7,] 54 0
## [8,] 14 0
## [9,] 70 0
## [10,] 92 0
## [11,] 64 0
## [12,] 92 0
## [13,] 56 0
## [14,] 38 0
## [15,] 64 0
## [16,] 49 0
## [17,] 105 0
## [18,] 62 0
## [19,] 107 0
## [20,] 77 0
## [21,] 81 0
## [22,] 50 0
## [23,] 78 0
## [24,] 102 0
## [25,] 98 0
## [26,] 70 0
## [27,] 102 0
## [28,] 82 0
## [29,] 64 0
## [30,] 86 0
## [31,] 52 0
## [32,] 49 0
## [33,] 90 0
## [34,] 62 0
## [35,] 31 0
## [36,] 77 1
## [37,] 37 1
## [38,] 103 1
## [39,] 82 1
## [40,] 105 1
## [41,] 42 1
## [42,] 61 1
## [43,] 86 1
## [44,] 84 1
## [45,] 63 1
## [46,] 90 1
## [47,] 39 1
## [48,] 59 1
## [49,] 82 1
## [50,] 82 1
## [51,] 71 1
## [52,] 71 1
## [53,] 86 1
## [54,] 70 1
## [55,] 74 1
## [56,] 73 1
## [57,] 91 0
## [58,] 106 0
## [59,] 73 0
## [60,] 77 0
## [61,] 80 0
## [62,] 49 0
## [63,] 78 0
## [64,] 75 0
## [65,] 60 0
## [66,] 106 0
## [67,] 44 0
## [68,] 85 0
## [69,] 79 0
## [70,] 84 0
## [71,] 104 0
## [72,] 12 0
## [73,] 52 0
## [74,] 98 0
## [75,] 85 0
## [76,] 95 0
## [77,] 79 1
## [78,] 106 1
## [79,] 81 1
## [80,] 55 1
## [81,] 101 1
## [82,] 65 1
## [83,] 72 1
## [84,] 55 1
## [85,] 65 1
## [86,] 71 1
## [87,] 82 1
## [88,] 84 1
## [89,] 95 1
## [90,] 95 1
## [91,] 91 1
## [92,] 57 1
## [93,] 87 1
## [94,] 40 1
## [95,] 91 1
## [96,] 50 1
## [97,] 25 1
## [98,] 73 1
## [99,] 63 0
## [100,] 50 0
## [101,] 54 0
## [102,] 73 0
## [103,] 8 0
## [104,] 53 0
## [105,] 65 0
## [106,] 58 0
## [107,] 24 0
## [108,] 64 0
## [109,] 106 0
## [110,] 61 0
## [111,] 66 0
## [112,] 79 0
## [113,] 74 0
## [114,] 69 0
## [115,] 103 0
## [116,] 52 0
## [117,] 93 0
## [118,] 94 0
## [119,] 91 0
## [120,] 57 0
## [121,] 94 0
## [122,] 79 0
## [123,] 62 0
## [124,] 86 0
## [125,] 49 0
## [126,] 14 0
## [127,] 100 0
## [128,] 50 0
## [129,] 79 0
## [130,] 77 0
## [131,] 50 0
## [132,] 73 0
## [133,] 96 0
## [134,] 87 0
## [135,] 41 0
## [136,] 54 0
## [137,] 84 0
## [138,] 67 0
## [139,] 53 0
## [140,] 104 0
## [141,] 86 0
## [142,] 102 0
## [143,] 50 0
## [144,] 42 0
## [145,] 52 0
## [146,] 107 0
## [147,] 92 0
## [148,] 52 0
## [149,] 69 0
## [150,] 82 0
## [151,] 101 0
## [152,] 64 0
## [153,] 55 0
## [154,] 98 0
## [155,] 56 0
## [156,] 91 0
## [157,] 51 0
## [158,] 102 0
## [159,] 71 0
## [160,] 13 0
## [161,] 11 0
## [162,] 53 0
## [163,] 82 0
## [164,] 89 0
## [165,] 56 0
## [166,] 54 0
## [167,] 72 0
## [168,] 102 0
## [169,] 51 0
## [170,] 100 0
## [171,] 62 0
## [172,] 73 0
## [173,] 84 0
## [174,] 87 0
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## [332,] 16 0
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## [334,] 70 0
## [335,] 68 0
## [336,] 81 0
## [337,] 67 0
## [338,] 67 0
## [339,] 97 1
## [340,] 60 1
## [341,] 86 1
## [342,] 75 1
## [343,] 59 1
## [344,] 87 1
## [345,] 75 1
## [346,] 72 1
## [347,] 102 1
## [348,] 101 1
## [349,] 68 1
## [350,] 80 1
## [351,] 104 1
## [352,] 61 1
## [353,] 41 1
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## [355,] 105 1
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## [365,] 107 1
## [366,] 73 1
## [367,] 91 1
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## [369,] 107 1
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## [376,] 90 1
## [377,] 57 1
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## [379,] 86 1
drop(scale(new_Cancer,center=center, scale=scale)%*%Cancer_pca$rotation[,1])
## [1] -1.441559363 0.466697152 1.724644704 -1.727412749 0.084534880
## [6] -0.987174108 -1.289312885 0.457476281 5.013544810 1.966110970
## [11] -1.709742154 1.323214712 -0.047344848 -0.023379894 1.042993427
## [16] -0.954171084 -0.510183493 0.248390384 -0.386424810 -0.212235416
## [21] 0.001291199 0.547237523 -0.581794885 1.484574719 0.730385134
## [26] 1.384044724 2.503197607 -1.094732396 -0.040233637 -0.913495245
## [31] 0.044817272 -1.310023914 -1.750326793 -0.860691537 1.293140200
## [36] -1.575412171 0.505620687 -1.445729993 -0.240634131 -0.335231355
## [41] 2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
## [46] 0.653344872 -0.903132282 -1.570956435 0.407142180 -2.095133885
## [51] 0.145196356 0.438754344 2.005777230 1.526981600 -1.762004433
## [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
## [61] -0.899762531 -1.006446958 -0.437812701 1.712300783 -1.263885916
## [66] -1.604219653 4.488026052 -0.665172931 -1.668377900 -1.130422629
## [71] 3.316812797 2.172380940 0.572326326 -1.827615023 0.720276568
## [76] 0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
## [81] 0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
## [86] 0.909892498 2.680823986 1.353531002 -1.678967186 -2.304099591
## [91] 0.741204117 -0.809147683 -0.790428226 1.549314451 -1.647991336
## [96] -0.268121798 -0.103534223 -0.776307350 1.103113756 -0.409442426
## [101] 4.633190126 -0.740349810 0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410 0.345220609 -1.364096376 -0.387521866 0.491580932
## [111] -1.087373932 1.210180885 1.869006469 0.492734252 0.889433533
## [116] -0.849321798 1.382626614 -0.876114257 0.129510618 0.006142764
## [121] -0.669636518 1.757579745 1.875711497 0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005 0.585398503 -1.786207788 -1.427017695 0.756062138
## [136] 0.145449916 -0.274324587 -0.438129117 1.064299809 2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125 0.505611656 0.247551976
## [146] -0.602802743 -1.272341157 2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156] 2.182293451 -0.839030427 -1.567211240 -0.656681669 1.746317858
## [161] 0.576848393 -1.591129974 -1.734769097 -1.257058960 0.171012852
## [166] 0.763873736 -0.648233872 4.075761272 0.108096807 -1.498040609
## [171] 0.047885996 1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176] 1.309706033 -0.190859319 -1.150520519 1.562083350 0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409 1.401099127 3.044609211
## [186] -0.608848019 0.869481448 -0.300778748 0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346 3.146400023
## [196] -1.646968799 0.194381857 1.355794604 0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892 1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734 0.691490501
## [211] 2.007551495 2.980951104 -0.051043670 -1.433696923 0.663189426
## [216] 2.031410016 0.789603453 0.673484381 -1.540903396 4.811125983
## [221] 2.960210184 0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172 2.040310983 1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583 0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213 3.689808324 0.637785394 6.741912903 -1.238593026
## [241] 0.823175506 0.046147404 -0.926653518 1.642861658 0.577872627
## [246] -1.754825326 -2.038325012 0.534102452 -0.778602587 -1.358620602
## [251] 0.552972231 0.160512695 -0.255760964 2.380048532 2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388 0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010 1.779574174 -0.692885384 -0.296827034
## [271] 2.648459041 -0.009329958 0.636626889 -0.730329225 0.329127497
## [276] -1.859016837 2.011187895 4.387657320 -1.562200265 1.140064695
## [281] -1.592089421 -0.863852065 1.027169030 -0.436517354 0.337411799
## [286] 0.922063650 0.074518204 0.517903752 1.205633993 5.667322803
## [291] 0.117634314 -1.257776898 -1.442594978 0.581815447 3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100 1.275367360
## [301] 0.510190648 0.497692443 -0.360524908 0.680162177 0.651993920
## [306] 3.788964776 0.324102302 1.241627938 -0.511968929 0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259 2.840965510 -1.178758036
## [316] -0.802177079 1.938258838 -1.084340607 5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619 2.150497872 0.219479185 -0.347437994
## [326] -0.234908136 0.016559745 -1.467247701 1.154836707 0.020892606
## [331] 0.169022729 0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802 1.016962553 1.874901202 -1.674481841 0.347838749
## [341] -0.523787799 -1.191298001 1.808772263 -1.770065768 -0.206433118
## [346] 0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351] 1.408443279 0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446 2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338 2.492171120 -0.327363502 -1.468296601
## [371] 0.644477407 4.369563022 -2.357052820 0.718708019 1.391878059
## [376] 0.905097897 3.157230391 0.003135705 -0.242056357
predict(Cancer_pca)[,1]
## [1] -1.441559363 0.466697152 1.724644704 -1.727412749 0.084534880
## [6] -0.987174108 -1.289312885 0.457476281 5.013544810 1.966110970
## [11] -1.709742154 1.323214712 -0.047344848 -0.023379894 1.042993427
## [16] -0.954171084 -0.510183493 0.248390384 -0.386424810 -0.212235416
## [21] 0.001291199 0.547237523 -0.581794885 1.484574719 0.730385134
## [26] 1.384044724 2.503197607 -1.094732396 -0.040233637 -0.913495245
## [31] 0.044817272 -1.310023914 -1.750326793 -0.860691537 1.293140200
## [36] -1.575412171 0.505620687 -1.445729993 -0.240634131 -0.335231355
## [41] 2.392046521 -1.496209472 -1.238156754 -0.122858339 -1.614959830
## [46] 0.653344872 -0.903132282 -1.570956435 0.407142180 -2.095133885
## [51] 0.145196356 0.438754344 2.005777230 1.526981600 -1.762004433
## [56] -1.584099552 -0.496130040 -0.310631363 -1.133478035 -1.203472671
## [61] -0.899762531 -1.006446958 -0.437812701 1.712300783 -1.263885916
## [66] -1.604219653 4.488026052 -0.665172931 -1.668377900 -1.130422629
## [71] 3.316812797 2.172380940 0.572326326 -1.827615023 0.720276568
## [76] 0.849193077 -0.640547040 -0.095120639 -0.045215749 -1.769164273
## [81] 0.718379560 -1.678008963 -0.895860760 -1.627068924 -1.331489281
## [86] 0.909892498 2.680823986 1.353531002 -1.678967186 -2.304099591
## [91] 0.741204117 -0.809147683 -0.790428226 1.549314451 -1.647991336
## [96] -0.268121798 -0.103534223 -0.776307350 1.103113756 -0.409442426
## [101] 4.633190126 -0.740349810 0.704221402 -0.385204834 -0.068793640
## [106] -0.692576410 0.345220609 -1.364096376 -0.387521866 0.491580932
## [111] -1.087373932 1.210180885 1.869006469 0.492734252 0.889433533
## [116] -0.849321798 1.382626614 -0.876114257 0.129510618 0.006142764
## [121] -0.669636518 1.757579745 1.875711497 0.312604564 -0.681074580
## [126] -0.863182056 -0.118572831 -1.423953866 -1.441335172 -0.856545337
## [131] -1.307398005 0.585398503 -1.786207788 -1.427017695 0.756062138
## [136] 0.145449916 -0.274324587 -0.438129117 1.064299809 2.098096298
## [141] -1.849943605 -0.732556857 -0.608595125 0.505611656 0.247551976
## [146] -0.602802743 -1.272341157 2.651497970 -1.824221268 -0.352147008
## [151] -1.129437762 -0.549974224 -1.104925141 -1.260493668 -1.263788087
## [156] 2.182293451 -0.839030427 -1.567211240 -0.656681669 1.746317858
## [161] 0.576848393 -1.591129974 -1.734769097 -1.257058960 0.171012852
## [166] 0.763873736 -0.648233872 4.075761272 0.108096807 -1.498040609
## [171] 0.047885996 1.337596168 -1.358485537 -1.872027381 -1.311243234
## [176] 1.309706033 -0.190859319 -1.150520519 1.562083350 0.457663612
## [181] -1.138195339 -0.007740653 -1.442466409 1.401099127 3.044609211
## [186] -0.608848019 0.869481448 -0.300778748 0.636747830 -1.117892469
## [191] -0.433517740 -2.074508151 -0.943857160 -0.671437346 3.146400023
## [196] -1.646968799 0.194381857 1.355794604 0.342080981 -0.390007297
## [201] -0.278709707 -0.042662340 -1.773111892 1.250439359 -1.763032603
## [206] -1.734908122 -0.040455138 -0.686284826 -0.444359734 0.691490501
## [211] 2.007551495 2.980951104 -0.051043670 -1.433696923 0.663189426
## [216] 2.031410016 0.789603453 0.673484381 -1.540903396 4.811125983
## [221] 2.960210184 0.548555090 -1.203818787 -0.095903547 -1.447284264
## [226] -0.721456172 2.040310983 1.855207556 -1.362709085 -0.288896751
## [231] -0.418601999 -1.163850583 0.411132602 -1.693135796 -1.469262447
## [236] -1.241804213 3.689808324 0.637785394 6.741912903 -1.238593026
## [241] 0.823175506 0.046147404 -0.926653518 1.642861658 0.577872627
## [246] -1.754825326 -2.038325012 0.534102452 -0.778602587 -1.358620602
## [251] 0.552972231 0.160512695 -0.255760964 2.380048532 2.562080786
## [256] -0.556325503 -1.361977024 -1.604168388 0.453544197 -0.245088734
## [261] -0.586494355 -0.595783004 -0.098509308 -1.732739711 -1.312518153
## [266] -1.117483636 -0.802242010 1.779574174 -0.692885384 -0.296827034
## [271] 2.648459041 -0.009329958 0.636626889 -0.730329225 0.329127497
## [276] -1.859016837 2.011187895 4.387657320 -1.562200265 1.140064695
## [281] -1.592089421 -0.863852065 1.027169030 -0.436517354 0.337411799
## [286] 0.922063650 0.074518204 0.517903752 1.205633993 5.667322803
## [291] 0.117634314 -1.257776898 -1.442594978 0.581815447 3.192976367
## [296] -1.664428065 -1.381280799 -0.359580844 -1.295214100 1.275367360
## [301] 0.510190648 0.497692443 -0.360524908 0.680162177 0.651993920
## [306] 3.788964776 0.324102302 1.241627938 -0.511968929 0.718039754
## [311] -0.310163020 -1.033055205 -0.764852259 2.840965510 -1.178758036
## [316] -0.802177079 1.938258838 -1.084340607 5.007927517 -0.352175349
## [321] -1.645893870 -0.723629619 2.150497872 0.219479185 -0.347437994
## [326] -0.234908136 0.016559745 -1.467247701 1.154836707 0.020892606
## [331] 0.169022729 0.596241854 -1.658882001 -1.130296134 -0.114349001
## [336] -1.180178802 1.016962553 1.874901202 -1.674481841 0.347838749
## [341] -0.523787799 -1.191298001 1.808772263 -1.770065768 -0.206433118
## [346] 0.781356058 -1.821829245 -0.284787326 -0.436832085 -1.217940564
## [351] 1.408443279 0.076806137 -1.371613972 -1.864312777 -1.989259900
## [356] -0.666931670 -0.752021652 -0.799705965 -1.601727166 -1.657122757
## [361] -0.384493964 -1.117824446 2.156938592 -0.789754021 -1.380570918
## [366] -1.291560292 -0.935262338 2.492171120 -0.327363502 -1.468296601
## [371] 0.644477407 4.369563022 -2.357052820 0.718708019 1.391878059
## [376] 0.905097897 3.157230391 0.003135705 -0.242056357
#The aboved two gives us the same thing. predict is a good function to know.
Cancer$Survivor <- as.factor(Cancer$Survivor)
out <- sapply(1:5, function(i){plot(Cancer$Survivor,Cancer_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Survivor")})
# Factor Analysis
#EFA
library(psych)
##
## Attaching package: 'psych'
## The following object is masked from 'package:car':
##
## logit
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
Cancer<- read.csv("~/Downloads/Cancer_Breast.csv")
attach(Cancer)
Cancer[1]
## Survivor
## 1 Alive
## 2 Alive
## 3 Alive
## 4 Alive
## 5 Alive
## 6 Alive
## 7 Alive
## 8 Dead
## 9 Alive
## 10 Alive
## 11 Dead
## 12 Alive
## 13 Alive
## 14 Alive
## 15 Alive
## 16 Alive
## 17 Alive
## 18 Alive
## 19 Alive
## 20 Alive
## 21 Alive
## 22 Alive
## 23 Alive
## 24 Alive
## 25 Alive
## 26 Alive
## 27 Alive
## 28 Alive
## 29 Alive
## 30 Alive
## 31 Alive
## 32 Alive
## 33 Alive
## 34 Alive
## 35 Alive
## 36 Alive
## 37 Alive
## 38 Alive
## 39 Alive
## 40 Alive
## 41 Dead
## 42 Alive
## 43 Alive
## 44 Alive
## 45 Alive
## 46 Alive
## 47 Dead
## 48 Alive
## 49 Alive
## 50 Alive
## 51 Alive
## 52 Alive
## 53 Alive
## 54 Alive
## 55 Alive
## 56 Alive
## 57 Alive
## 58 Alive
## 59 Alive
## 60 Alive
## 61 Alive
## 62 Alive
## 63 Alive
## 64 Alive
## 65 Dead
## 66 Alive
## 67 Dead
## 68 Alive
## 69 Alive
## 70 Alive
## 71 Alive
## 72 Dead
## 73 Alive
## 74 Alive
## 75 Alive
## 76 Alive
## 77 Alive
## 78 Alive
## 79 Alive
## 80 Alive
## 81 Alive
## 82 Alive
## 83 Alive
## 84 Alive
## 85 Alive
## 86 Alive
## 87 Alive
## 88 Alive
## 89 Alive
## 90 Alive
## 91 Dead
## 92 Alive
## 93 Dead
## 94 Dead
## 95 Alive
## 96 Alive
## 97 Dead
## 98 Alive
## 99 Dead
## 100 Alive
## 101 Dead
## 102 Alive
## 103 Alive
## 104 Dead
## 105 Alive
## 106 Alive
## 107 Dead
## 108 Alive
## 109 Alive
## 110 Alive
## 111 Alive
## 112 Dead
## 113 Alive
## 114 Alive
## 115 Alive
## 116 Alive
## 117 Alive
## 118 Alive
## 119 Alive
## 120 Alive
## 121 Alive
## 122 Alive
## 123 Alive
## 124 Alive
## 125 Alive
## 126 Dead
## 127 Alive
## 128 Alive
## 129 Alive
## 130 Alive
## 131 Alive
## 132 Alive
## 133 Alive
## 134 Alive
## 135 Dead
## 136 Dead
## 137 Alive
## 138 Dead
## 139 Dead
## 140 Alive
## 141 Alive
## 142 Alive
## 143 Alive
## 144 Dead
## 145 Dead
## 146 Alive
## 147 Alive
## 148 Dead
## 149 Alive
## 150 Alive
## 151 Alive
## 152 Alive
## 153 Dead
## 154 Alive
## 155 Alive
## 156 Alive
## 157 Alive
## 158 Alive
## 159 Alive
## 160 Dead
## 161 Alive
## 162 Alive
## 163 Alive
## 164 Alive
## 165 Alive
## 166 Alive
## 167 Alive
## 168 Alive
## 169 Alive
## 170 Alive
## 171 Dead
## 172 Alive
## 173 Alive
## 174 Alive
## 175 Alive
## 176 Alive
## 177 Dead
## 178 Alive
## 179 Alive
## 180 Dead
## 181 Alive
## 182 Dead
## 183 Dead
## 184 Alive
## 185 Alive
## 186 Alive
## 187 Alive
## 188 Alive
## 189 Dead
## 190 Alive
## 191 Alive
## 192 Alive
## 193 Alive
## 194 Alive
## 195 Alive
## 196 Alive
## 197 Alive
## 198 Alive
## 199 Alive
## 200 Alive
## 201 Alive
## 202 Alive
## 203 Dead
## 204 Dead
## 205 Alive
## 206 Alive
## 207 Alive
## 208 Alive
## 209 Alive
## 210 Alive
## 211 Alive
## 212 Dead
## 213 Alive
## 214 Alive
## 215 Alive
## 216 Dead
## 217 Dead
## 218 Alive
## 219 Alive
## 220 Dead
## 221 Dead
## 222 Dead
## 223 Alive
## 224 Alive
## 225 Alive
## 226 Alive
## 227 Alive
## 228 Alive
## 229 Alive
## 230 Alive
## 231 Alive
## 232 Alive
## 233 Alive
## 234 Alive
## 235 Alive
## 236 Alive
## 237 Alive
## 238 Alive
## 239 Dead
## 240 Alive
## 241 Dead
## 242 Alive
## 243 Alive
## 244 Alive
## 245 Alive
## 246 Alive
## 247 Alive
## 248 Dead
## 249 Alive
## 250 Alive
## 251 Alive
## 252 Alive
## 253 Alive
## 254 Alive
## 255 Alive
## 256 Alive
## 257 Alive
## 258 Alive
## 259 Alive
## 260 Alive
## 261 Alive
## 262 Alive
## 263 Alive
## 264 Dead
## 265 Alive
## 266 Alive
## 267 Alive
## 268 Alive
## 269 Dead
## 270 Alive
## 271 Dead
## 272 Alive
## 273 Alive
## 274 Alive
## 275 Alive
## 276 Alive
## 277 Alive
## 278 Dead
## 279 Alive
## 280 Alive
## 281 Alive
## 282 Alive
## 283 Dead
## 284 Alive
## 285 Alive
## 286 Dead
## 287 Alive
## 288 Alive
## 289 Alive
## 290 Dead
## 291 Alive
## 292 Alive
## 293 Dead
## 294 Alive
## 295 Alive
## 296 Alive
## 297 Alive
## 298 Alive
## 299 Alive
## 300 Alive
## 301 Alive
## 302 Alive
## 303 Alive
## 304 Alive
## 305 Alive
## 306 Dead
## 307 Alive
## 308 Alive
## 309 Alive
## 310 Alive
## 311 Alive
## 312 Alive
## 313 Alive
## 314 Dead
## 315 Alive
## 316 Alive
## 317 Alive
## 318 Alive
## 319 Alive
## 320 Alive
## 321 Alive
## 322 Alive
## 323 Alive
## 324 Alive
## 325 Alive
## 326 Alive
## 327 Alive
## 328 Alive
## 329 Alive
## 330 Alive
## 331 Alive
## 332 Dead
## 333 Alive
## 334 Alive
## 335 Alive
## 336 Alive
## 337 Alive
## 338 Alive
## 339 Alive
## 340 Alive
## 341 Alive
## 342 Alive
## 343 Alive
## 344 Alive
## 345 Alive
## 346 Alive
## 347 Alive
## 348 Alive
## 349 Alive
## 350 Alive
## 351 Alive
## 352 Alive
## 353 Alive
## 354 Alive
## 355 Alive
## 356 Alive
## 357 Alive
## 358 Dead
## 359 Alive
## 360 Alive
## 361 Alive
## 362 Alive
## 363 Dead
## 364 Dead
## 365 Alive
## 366 Alive
## 367 Alive
## 368 Alive
## 369 Alive
## 370 Dead
## 371 Alive
## 372 Dead
## 373 Alive
## 374 Alive
## 375 Alive
## 376 Alive
## 377 Alive
## 378 Alive
## 379 Alive
fit.pc <- principal(Cancer[-1], nfactors=5, rotate="varimax")
fit.pc
## Principal Components Analysis
## Call: principal(r = Cancer[-1], nfactors = 5, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC5 RC4 RC3 h2 u2 com
## Age -0.11 -0.03 0.01 0.99 0.01 1.00 0.00067 1.0
## Stage 0.94 0.07 0.00 -0.07 -0.03 0.89 0.10629 1.0
## Tumor.Size 0.93 0.12 -0.09 -0.07 0.00 0.89 0.10621 1.1
## Regional.Node.Examined -0.05 0.91 0.06 0.01 -0.06 0.83 0.16842 1.0
## Reginol.Node.Positive 0.37 0.73 -0.17 -0.07 0.04 0.70 0.29643 1.6
## Survival.Months -0.06 -0.04 0.99 0.01 0.06 0.99 0.01323 1.0
## Sex -0.02 -0.03 0.06 0.01 1.00 1.00 0.00318 1.0
##
## RC1 RC2 RC5 RC4 RC3
## SS loadings 1.90 1.38 1.02 1.00 1.00
## Proportion Var 0.27 0.20 0.15 0.14 0.14
## Cumulative Var 0.27 0.47 0.61 0.76 0.90
## Proportion Explained 0.30 0.22 0.16 0.16 0.16
## Cumulative Proportion 0.30 0.52 0.68 0.84 1.00
##
## Mean item complexity = 1.1
## Test of the hypothesis that 5 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.06
## with the empirical chi square 58.1 with prob < NA
##
## Fit based upon off diagonal values = 0.94
round(fit.pc$values, 3)
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
#Infernce
# In the round function we can infer that there are six eigenvalues displayed in descending order.
fit.pc$loadings
##
## Loadings:
## RC1 RC2 RC5 RC4 RC3
## Age -0.106 0.993
## Stage 0.939
## Tumor.Size 0.931 0.118
## Regional.Node.Examined 0.906
## Reginol.Node.Positive 0.370 0.730 -0.167
## Survival.Months 0.989
## Sex 0.996
##
## RC1 RC2 RC5 RC4 RC3
## SS loadings 1.904 1.377 1.021 1.002 1.002
## Proportion Var 0.272 0.197 0.146 0.143 0.143
## Cumulative Var 0.272 0.469 0.615 0.758 0.901
# Loadings with more digits
for (i in c(1,3,2,4)) { print(fit.pc$loadings[[1,i]])}
## [1] -0.1063485
## [1] 0.007309789
## [1] -0.03169656
## [1] 0.9933908
# Communalities
fit.pc$communality
## Age Stage Tumor.Size
## 0.9993287 0.8937139 0.8937913
## Regional.Node.Examined Reginol.Node.Positive Survival.Months
## 0.8315783 0.7035652 0.9867685
## Sex
## 0.9968239
## The output shows the communality values for each variable in the dataset. The values range from 0 to 1, with higher values indicating that a greater proportion of the variance.
## The variable "Age" has a communality value of 0.9993287, indicating that almost all of the variance in age can be explained by the other variables in the model. Similarly, the variables "Stage", "Tumor.Size", and "Survival.Months" all have high communality values.
## On the other hand, the variables "Regional.Node.Examined" and "Reginol.Node.Positive" have lower communality values.
# Rotated factor scores, Notice the columns ordering: RC1, RC3, RC2 and RC4
fit.pc$scores
## RC1 RC2 RC5 RC4 RC3
## [1,] -1.307322343 0.720541453 -0.4109466207 1.432199590 -0.5995915
## [2,] 0.125258717 -0.005991665 -0.3960011664 -0.446560393 -0.5032814
## [3,] 1.521528245 0.036535290 0.2675298647 0.576373054 -0.5207671
## [4,] -0.576956591 -1.270969616 0.3457891320 0.284757521 -0.5355061
## [5,] 0.356003626 -1.429130282 -1.0038777695 -0.793721798 -0.4937427
## [6,] -0.898825264 0.255382282 0.7824421029 -0.435014544 -0.5902173
## [7,] -1.123345808 -0.495508261 -0.8492879225 -0.480027023 -0.5198397
## [8,] -0.166918910 -0.929718498 -2.5074915609 -1.569559540 -0.4551006
## [9,] 2.895698210 1.407000989 0.0701621060 -1.232915129 -0.3627589
## [10,] 1.623286547 1.166469031 1.1339661602 1.804724621 -0.5607949
## [11,] -0.796737103 -0.643134432 -0.4467304353 1.405298813 -0.5386135
## [12,] 1.383407566 -0.613812751 1.0606014044 -0.771008966 -0.5964824
## [13,] 0.231378332 -0.277381746 -0.6480718231 1.212891868 -0.5306287
## [14,] -1.209097244 1.129275448 -1.4960382009 -0.757923760 -0.4399465
## [15,] 0.332062691 1.089576672 -0.4600933919 0.880089204 -0.3798997
## [16,] -1.005709045 0.294230470 -0.9459212280 0.683789562 -0.5499190
## [17,] 0.744674990 -1.521478193 1.3942774551 0.198005816 -0.5882018
## [18,] -0.392840627 0.331740014 -0.2023918755 -1.219299086 -0.6020107
## [19,] -0.070089438 -0.131860914 1.6981587841 -0.691186435 -0.6608646
## [20,] -0.051436133 0.191789657 0.4212599841 0.665104459 -0.6298133
## [21,] -0.006732381 -0.175158552 0.5162044500 -0.678069438 -0.5910345
## [22,] 0.235767119 0.064736618 -0.9160969551 0.345887419 -0.4880382
## [23,] 0.238416634 -1.252012775 0.2398637050 0.059950918 -0.5605271
## [24,] 1.485603522 -0.192706771 1.6426949223 -0.500072971 -0.6715799
## [25,] -0.638645746 2.989208025 0.9036488179 0.790027137 -0.3283707
## [26,] -0.178437490 2.777908908 -0.0413468810 1.003449656 -0.4138383
## [27,] 0.582909298 2.785940166 1.1903597199 -0.617407633 -0.3249590
## [28,] -0.958925042 -0.214668978 0.4376328731 -1.006550454 -0.5747757
## [29,] -0.030712394 -0.064531047 -0.2958902002 0.303786095 -0.5331017
## [30,] 0.068379476 -0.661628273 0.6696875518 1.275338778 -0.6122729
## [31,] 0.341019051 -1.423515415 -0.9156870304 -0.796564772 -0.4978896
## [32,] -0.849797464 -1.056311111 -1.1560432828 -0.259833717 -0.4831038
## [33,] -0.695855576 -0.893221994 0.6669447747 0.399805322 -0.5655454
## [34,] -0.904371285 0.418390526 -0.4227821023 0.568333687 -0.5359795
## [35,] -0.134717535 0.896879252 -1.7893854324 -0.883820975 -0.3884290
## [36,] -0.962782744 -0.496271026 0.0146280532 -0.506395204 1.8698186
## [37,] -0.216070538 0.760054595 -1.5310060164 -0.017108670 1.9268830
## [38,] -0.822162376 -0.027741225 1.2379223356 -0.475255516 1.8060242
## [39,] 0.207377292 -0.584119832 0.3835243419 -0.591160486 1.8359579
## [40,] -0.015945155 0.231547364 1.4102652463 -0.390085871 1.8134154
## [41,] 1.672295634 0.331889914 -1.4195501472 0.458760335 2.0373001
## [42,] -0.810396953 -0.246830664 -0.6575095163 0.962169014 1.8807243
## [43,] 0.192702901 -1.337412693 0.4521697808 0.787065016 1.8300087
## [44,] -0.045240073 0.301893642 0.4610586322 -0.165708418 1.8659211
## [45,] -1.114592031 -0.318549810 -0.5798944449 -0.067077011 1.8811846
## [46,] 1.433075757 -0.404070935 0.7973567945 1.398145800 1.8307848
## [47,] -1.300369551 -0.028825995 -1.5735162921 -1.478447862 1.9188192
## [48,] -0.890968449 -0.347396610 -0.7258310349 0.737085989 1.8686802
## [49,] 0.161477066 0.663117873 0.3316500047 -0.142306077 1.9180601
## [50,] -0.856746942 -0.435474034 0.1880548609 1.468182616 1.8657762
## [51,] -0.312541977 0.136516082 -0.0161195165 -1.924986682 1.8441573
## [52,] 1.447543637 -0.924569775 0.0183976951 1.743586990 1.8054576
## [53,] 2.812048369 -1.262055827 0.6755524008 0.899216739 1.8278901
## [54,] 1.638406126 0.094433947 0.1223316011 1.168921857 1.7927188
## [55,] -1.245588504 0.059259832 -0.0048643311 0.161759900 1.8212159
## [56,] -1.016071990 -0.238010351 -0.0883995005 -0.046799422 1.8419097
## [57,] -0.055136450 0.137116743 1.0235735974 0.870721586 -0.6544031
## [58,] -1.556238684 2.969335661 1.9976509472 -0.452852539 -0.7682586
## [59,] -1.012521694 -0.126699947 0.0506202835 -0.563961013 -0.5666070
## [60,] -1.045300388 0.174424312 0.2326398439 -0.013173329 -0.5713923
## [61,] -1.047075348 0.794048712 0.4663384322 0.134380248 -0.6038729
## [62,] -0.970723754 -0.436290566 -1.0538337127 -0.453609592 -0.5102184
## [63,] 0.122295878 -1.536193908 0.2054873223 -1.395765740 -0.5403993
## [64,] 1.581638643 0.050824165 0.4515941633 0.740198573 -0.6202844
## [65,] -0.932273302 0.175827417 -0.5609552382 1.316333715 -0.5283159
## [66,] -0.743337478 -0.980885386 1.3694624000 -1.044983239 -0.5811547
## [67,] 1.390940985 2.318833021 -1.2599663894 -2.372541212 -0.2246068
## [68,] -1.139281898 0.521706170 0.6217134196 -1.658294503 -0.5704799
## [69,] -0.716585571 -1.001628675 0.1669302103 0.287943533 -0.5407599
## [70,] -0.828120721 -0.182566987 0.4547620386 -0.351044576 -0.5421598
## [71,] 2.984339506 -0.185413879 1.5250696791 -0.266452072 -0.5065661
## [72,] 0.099828289 2.328900874 -2.7615939453 1.129436991 -0.2258636
## [73,] -0.279414997 -0.258351242 -0.7204289427 -2.549928342 -0.5470274
## [74,] -0.900858304 -0.047990019 1.1433603243 1.189652443 -0.6255749
## [75,] 0.134925139 1.631172172 0.4663292758 1.405408589 -0.4089834
## [76,] 1.325986367 -0.600452614 1.2520818000 0.333261835 -0.6514159
## [77,] 0.149994138 -0.245884510 0.2121614860 1.267497207 1.8519088
## [78,] 0.576780408 -0.966039415 1.4297089883 -1.341977353 1.8022253
## [79,] 0.541371992 -0.809300150 0.3464211791 -0.334948836 1.8326476
## [80,] -0.787355976 -0.612567340 -0.9499943025 1.392111130 1.8843995
## [81,] 0.132644569 1.542881672 1.1662494527 -0.137898033 1.9254658
## [82,] -0.682845547 -0.521869545 -0.4915264667 1.295203261 1.8654899
## [83,] 0.077842632 -0.626853150 -0.0884163446 1.256550128 1.8394374
## [84,] -0.775710231 -1.267010626 -1.0394945328 -0.290422278 1.9244288
## [85,] -0.991683414 -0.267371856 -0.4382882639 -0.478076329 1.8612840
## [86,] 0.346915202 0.452886041 -0.2433999789 -0.909675645 1.9959419
## [87,] 2.753852714 -0.892367861 0.4306068673 -0.431274113 1.9073869
## [88,] 1.836790459 -0.907765459 0.6259591234 -0.074988319 1.8029850
## [89,] -0.784136825 -0.399092767 0.8572468103 -0.042470426 1.8138463
## [90,] -0.946486640 -0.525802857 0.8179522029 1.023057519 1.8078354
## [91,] 1.489750527 -1.023991747 0.9011815124 -0.021555720 1.7873922
## [92,] -1.237649670 -0.128579032 -0.7507014145 -2.464537055 1.8792844
## [93,] 0.292157036 -0.780090543 0.4823621758 0.917137216 1.8654414
## [94,] -0.178260355 1.745556406 -1.5841080146 -1.026775673 2.0864486
## [95,] -0.855501286 -0.097546934 0.6522412563 0.390133410 1.8433368
## [96,] -0.143540138 0.039741610 -0.9415753167 0.629886224 1.8511461
## [97,] 0.067327304 -1.195942177 -2.2248580614 -0.501726227 1.9608656
## [98,] 0.063292598 -0.650918461 -0.0063650523 0.714526042 1.8225174
## [99,] 1.438480931 -1.398980993 -0.2220053612 -0.363030537 -0.5672187
## [100,] 0.022209305 -0.369532856 -0.8648449930 1.531062537 -0.5623492
## [101,] 1.290735390 3.343340679 -0.6987257017 -1.568284666 -0.2738182
## [102,] -1.225362823 0.763522764 0.1962778723 -0.861187254 -0.6062367
## [103,] 0.244231108 -1.517589366 -2.8543340721 -1.661375921 -0.4101860
## [104,] 0.078282248 -1.012468615 -0.8245627928 0.290624553 -0.5305240
## [105,] -0.129068709 -0.165668032 -0.2293994506 -0.253836904 -0.5484729
## [106,] 0.181475413 -1.443499081 -0.6777455520 0.600597596 -0.5215860
## [107,] 0.154709264 -0.736066390 -2.0442414060 0.009064502 -0.4860097
## [108,] -0.697468850 -0.292429402 -0.4211980396 1.431482529 -0.5315644
## [109,] -0.064796549 -0.759694348 1.5263602516 -1.834169815 -0.6044506
## [110,] -0.102736786 1.250802936 -0.1817599562 1.048005947 -0.6095626
## [111,] -0.911159339 0.181480103 -0.3245823391 0.649678621 -0.5142309
## [112,] 1.263393891 -1.347298151 0.3756429440 -1.810192301 -0.5372158
## [113,] 0.099961479 2.258916113 0.3318487687 -0.793842096 -0.5187524
## [114,] 0.265346964 -0.326719527 -0.0228867444 -0.973960318 -0.5550197
## [115,] 1.453520563 -0.813470081 1.4293107845 0.074682844 -0.5731179
## [116,] -0.872120563 -0.235055775 -0.9604664732 -0.229531597 -0.4840017
## [117,] 1.788536862 -1.026488867 1.1158405739 -0.291301779 -0.6154798
## [118,] -0.577131613 0.808464286 0.8277395449 1.543781499 -0.4914876
## [119,] 0.142446189 -0.073395943 0.9404550905 -0.668364310 -0.5904370
## [120,] -0.096023689 -0.195741294 -0.5493823082 -0.127753610 -0.5527860
## [121,] 0.470777695 -0.853494484 0.9640285036 1.408655642 -0.5912659
## [122,] 1.405049166 -0.336954364 0.6651494977 -1.074659082 -0.6360513
## [123,] 0.563183638 1.225899485 -0.5745497212 -0.412018571 -0.3279408
## [124,] 0.137527966 0.747763928 0.8076285109 0.582272820 -0.6052919
## [125,] -1.207472037 0.659121375 -0.9173575548 -0.202538944 -0.5431849
## [126,] -1.059365232 -0.111863156 -2.5520963763 0.783045168 -0.4715829
## [127,] -0.093593367 -0.328386090 1.3329439631 -1.696361488 -0.6132991
## [128,] -0.668485812 -1.234189812 -1.1437986452 0.407393990 -0.4784974
## [129,] -0.781412414 -0.636562877 0.1921706334 0.075484452 -0.5360648
## [130,] -0.910852125 -0.118141856 0.1648322582 -1.118686080 -0.5283327
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## [227,] 1.266507000 0.767534233 -0.3503472066 0.692688427 -0.4909861
## [228,] 0.526231893 1.970061816 0.3846572483 0.309208920 -0.7235692
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## [289,] -0.679085140 3.954507874 0.5752992943 1.453201950 -0.2448900
## [290,] 2.470404344 2.991945738 -0.5290849496 -1.029346539 -0.4106261
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## [313,] -0.895696902 0.278400309 -0.2835395432 -0.127721411 -0.4762479
## [314,] 1.378787835 2.228549730 1.1028844251 0.377888253 -0.4504376
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## [329,] 1.888859941 -1.054748117 1.0499863677 0.811763660 -0.6672029
## [330,] 0.228124222 0.115515456 0.6542582753 0.614143857 -0.4835419
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## [332,] -0.323716119 0.089322447 -2.3012144370 -0.658113240 -0.4916334
## [333,] -0.573599036 -0.673945940 1.3808133533 0.399976500 -0.5632159
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## [335,] 0.067385310 -0.470299644 -0.0712174729 -0.123049056 -0.5774999
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## [337,] 1.498468230 -1.471211322 -0.1108668839 -0.120909521 -0.5573615
## [338,] 2.034240811 -0.624734880 -0.0001672349 0.977509078 -0.5696230
## [339,] -0.941394422 0.554847796 1.0125561096 1.183788414 1.7975113
## [340,] 0.116552431 -0.162234038 -0.5812925108 -1.016758341 1.8988221
## [341,] -0.073108062 -0.258456641 0.5642638902 -0.288911824 1.8266773
## [342,] -1.095299260 1.140502682 -0.0782396875 1.271318757 1.9275930
## [343,] 1.302176223 -0.312844591 -0.3730818043 -1.400463413 1.8215573
## [344,] -0.998956914 -0.576689506 0.4762144801 -0.623029529 1.8354088
## [345,] -0.166864133 0.930549169 0.1879962742 1.188073661 1.8234945
## [346,] 0.444933776 0.569084471 -0.2248211922 0.085279123 2.0038440
## [347,] -0.793884694 -0.930738805 1.0855863176 -0.958327240 1.8299915
## [348,] 0.076643584 -0.008551844 1.3088948879 -0.582715582 1.7746895
## [349,] -1.384810454 1.995909568 -0.2337161697 -0.236952360 1.9093380
## [350,] -0.934572665 0.209784179 0.2624276064 -0.240002684 1.8334865
## [351,] 0.994896423 0.734903211 1.6522061698 -0.990509561 1.7462317
## [352,] 0.011956605 0.139481088 -0.5020461494 -0.026141451 1.8748573
## [353,] -0.938648886 -0.930231873 -1.6000667152 -0.498723797 1.9336654
## [354,] -0.975524130 -0.740678639 1.0250360445 -1.077007603 1.8226366
## [355,] -0.723077419 -1.282766287 1.1606939574 -0.974269193 1.8409410
## [356,] -0.171118857 0.065130684 -0.6052809737 1.508045589 1.8105869
## [357,] -1.105820530 0.706046414 -0.5775661326 -0.543795765 1.8492150
## [358,] 0.199909474 -1.022116250 -0.9413885677 1.367514283 1.8902877
## [359,] -0.766697782 -1.157875422 -0.0920143761 -0.952566415 1.8869981
## [360,] -0.935248613 0.416620219 0.4014957360 1.422645689 1.7891634
## [361,] -0.034142609 -0.592841094 -0.9056044060 0.053421438 1.8787911
## [362,] -1.020311568 0.667748213 1.3451742682 -0.882893500 1.7576795
## [363,] 1.503081995 0.497724205 -0.8508028245 0.418045118 1.8398103
## [364,] 0.339567925 -1.258668199 1.0621879893 -0.411355661 1.8331884
## [365,] -0.878881317 -0.303149718 1.3785128159 -1.597249351 1.8173742
## [366,] -0.738203710 0.326579074 -0.1093419712 1.310637661 1.8736257
## [367,] -0.844541325 0.913100228 0.6777806934 0.311159619 1.8810449
## [368,] 2.206718168 1.120359115 1.0545424190 1.675635597 1.8372605
## [369,] 0.478510000 0.020594005 1.4993742541 0.979616572 1.7993268
## [370,] -0.655552750 0.197720065 0.3232111057 1.505296670 1.8972806
## [371,] -0.170573823 2.157417514 0.7973523682 0.546617198 1.8702915
## [372,] 3.055471856 0.696475884 0.0263444609 -0.807508660 1.9940047
## [373,] -0.592689309 -1.166518230 1.0294289591 1.021432409 1.8295919
## [374,] -0.096223023 0.811249314 -0.9120283373 -0.644753711 1.8706498
## [375,] -0.345022305 1.918486831 -0.6107381920 -1.678122770 1.9867217
## [376,] 0.576369263 0.862717139 0.5818314310 0.099965846 1.9815445
## [377,] 2.198335581 0.451180405 -0.7156699293 -0.242911092 2.0216293
## [378,] -0.190824950 0.066575923 0.5876761560 -1.704525215 1.8227795
## [379,] -0.066038449 0.053964866 0.6929418915 -0.577618988 1.7762757
# Play with FA utilities
fa.parallel(Cancer[-1]) # See factor recommendation
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1
# Inference
# fa.parallel(Cancer[-1]) is performing a parallel analysis on the Cancer data set, excluding the Survivor variable. In a resulting scree plot we can compare the eigenvalues of the original data set to the mean and percentile values of the eigenvalues of the simulated data sets. The point at which the eigenvalues of the original data set intersect the mean or percentile values of the eigenvalues of the simulated data sets is a suggestion for the number of factors to retain.
fa.plot(fit.pc) # See Correlations within Factors
fa.diagram(fit.pc) # Visualize the relationship
vss(Cancer[-1]) # See Factor recommendations for a simple structure
##
## Very Simple Structure
## Call: vss(x = Cancer[-1])
## VSS complexity 1 achieves a maximimum of 0.74 with 4 factors
## VSS complexity 2 achieves a maximimum of 0.81 with 4 factors
##
## The Velicer MAP achieves a minimum of 0.07 with 1 factors
## BIC achieves a minimum of -36.66 with 2 factors
## Sample Size adjusted BIC achieves a minimum of -11.28 with 2 factors
##
## Statistics by number of factors
## vss1 vss2 map dof chisq prob sqresid fit RMSEA BIC SABIC complex
## 1 0.49 0.00 0.072 14 9.4e+01 7.6e-14 4.8 0.49 0.123 11 55.0 1.0
## 2 0.54 0.61 0.079 8 1.1e+01 2.1e-01 3.7 0.61 0.031 -37 -11.3 1.3
## 3 0.64 0.73 0.144 3 2.2e+00 5.3e-01 2.4 0.74 0.000 -16 -6.1 1.3
## 4 0.74 0.81 0.272 -1 8.9e-02 NA 1.7 0.82 NA NA NA 1.1
## 5 0.62 0.66 0.555 -4 1.6e-09 NA 2.5 0.74 NA NA NA 1.4
## 6 0.60 0.68 1.000 -6 1.6e-12 NA 2.6 0.73 NA NA NA 1.4
## 7 0.60 0.68 NA -7 1.6e-12 NA 2.6 0.73 NA NA NA 1.4
## eChisq SRMR eCRMS eBIC
## 1 1.1e+02 8.3e-02 0.102 26
## 2 1.2e+01 2.7e-02 0.044 -36
## 3 1.5e+00 9.8e-03 0.026 -16
## 4 1.0e-01 2.5e-03 NA NA
## 5 5.8e-10 1.9e-07 NA NA
## 6 5.1e-13 5.7e-09 NA NA
## 7 5.1e-13 5.7e-09 NA NA
# Computing Correlation Matrix
corrm.emp <- cor(Cancer[-1])
corrm.emp
## Age Stage Tumor.Size
## Age 1.00000000 -0.17789979 -0.17541686
## Stage -0.17789979 1.00000000 0.80790600
## Tumor.Size -0.17541686 0.80790600 1.00000000
## Regional.Node.Examined -0.02396398 0.07501922 0.09516337
## Reginol.Node.Positive -0.11813829 0.34012221 0.39022509
## Survival.Months 0.02531278 -0.08063557 -0.15100312
## Sex 0.02509020 -0.04136117 -0.02522026
## Regional.Node.Examined Reginol.Node.Positive
## Age -0.02396398 -0.11813829
## Stage 0.07501922 0.34012221
## Tumor.Size 0.09516337 0.39022509
## Regional.Node.Examined 1.00000000 0.40692674
## Reginol.Node.Positive 0.40692674 1.00000000
## Survival.Months -0.02528933 -0.15699916
## Sex -0.06026009 -0.03344945
## Survival.Months Sex
## Age 0.02531278 0.02509020
## Stage -0.08063557 -0.04136117
## Tumor.Size -0.15100312 -0.02522026
## Regional.Node.Examined -0.02528933 -0.06026009
## Reginol.Node.Positive -0.15699916 -0.03344945
## Survival.Months 1.00000000 0.10999706
## Sex 0.10999706 1.00000000
#Inference
# The correlation matrix shows that all variables are moderately to strongly correlated with each other, indicating that there is some redundancy in the data.
plot(corrm.emp)
Cancer_pca <- prcomp(Cancer[-1], scale=TRUE)
summary(Cancer_pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.4983 1.0852 1.0303 0.9698 0.9387 0.71218 0.43271
## Proportion of Variance 0.3207 0.1682 0.1516 0.1344 0.1259 0.07246 0.02675
## Cumulative Proportion 0.3207 0.4889 0.6406 0.7749 0.9008 0.97325 1.00000
# Inference
# From the summary statistics, we can see that the first principal component (PC1) explains 32.07% of the total variance, the second principal component (PC2) explains 16.82%, and so on. The first two principal components (PC1 and PC2) together explain 48.89% of the total variance. The cumulative proportion reaches 97.33% after the sixth principal component (PC6), meaning that the remaining principal components explain very little additional variance in the data.
plot(Cancer_pca)
# A table containing eigenvalues and %'s accounted, follows. Eigenvalues are the sdev^2
(eigen_Cancer <- round(Cancer_pca$sdev^2,3))
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
round(fit.pc$values, 3)
## [1] 2.245 1.178 1.061 0.941 0.881 0.507 0.187
names(eigen_Cancer) <- paste("PC",1:6,sep="")
eigen_Cancer
## PC1 PC2 PC3 PC4 PC5 PC6 <NA>
## 2.245 1.178 1.061 0.941 0.881 0.507 0.187
sumlambdas <- sum(eigen_Cancer)
sumlambdas
## [1] 7
## Inference
# sumlambdas is equal to 7, this suggests that the PCA extracted 7 principal components from the data, and that the sum of their corresponding eigenvalues explains all of the variation in the data.
propvar <- round(eigen_Cancer/sumlambdas,2)
propvar
## PC1 PC2 PC3 PC4 PC5 PC6 <NA>
## 0.32 0.17 0.15 0.13 0.13 0.07 0.03
cumvar_Cancer <- cumsum(propvar)
cumvar_Cancer
## PC1 PC2 PC3 PC4 PC5 PC6 <NA>
## 0.32 0.49 0.64 0.77 0.90 0.97 1.00
matlambdas <- rbind(eigen_Cancer,propvar,cumvar_Cancer)
matlambdas
## PC1 PC2 PC3 PC4 PC5 PC6 <NA>
## eigen_Cancer 2.245 1.178 1.061 0.941 0.881 0.507 0.187
## propvar 0.320 0.170 0.150 0.130 0.130 0.070 0.030
## cumvar_Cancer 0.320 0.490 0.640 0.770 0.900 0.970 1.000
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
rownames(matlambdas)
## [1] "Eigenvalues" "Prop. variance" "Cum. prop. variance"
eigvec.emp <- Cancer_pca$rotation
print(Cancer_pca)
## Standard deviations (1, .., p=7):
## [1] 1.4982562 1.0851943 1.0302880 0.9698062 0.9386874 0.7121769 0.4327057
##
## Rotation (n x k) = (7 x 7):
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor.Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional.Node.Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol.Node.Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival.Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6 PC7
## Age -0.41336263 -0.03629602 -0.00410619
## Stage -0.21766761 0.18269976 -0.69082826
## Tumor.Size -0.13361696 0.13694401 0.71864375
## Regional.Node.Examined -0.03947383 0.57624593 0.00365182
## Reginol.Node.Positive 0.10540722 -0.76394463 -0.04789123
## Survival.Months -0.63971799 -0.15748760 0.05900235
## Sex 0.58479969 0.07795267 -0.02241484
# Taking the first four PCs to generate linear combinations for all the variables with four factors
pcafactors.emp <- eigvec.emp[,1:6]
pcafactors.emp
## PC1 PC2 PC3 PC4
## Age -0.21487519 0.2043145 0.027261393 0.85973142
## Stage 0.56017028 -0.3373169 0.011318788 0.11956737
## Tumor.Size 0.57902017 -0.2934857 -0.007289973 0.15966422
## Regional.Node.Examined 0.23910247 0.6987477 0.329462796 -0.11137816
## Reginol.Node.Positive 0.45785153 0.3946611 0.191113542 0.03278061
## Survival.Months -0.18008353 -0.1898301 0.618720758 -0.33346116
## Sex -0.07446786 -0.2798176 0.686432853 0.31047844
## PC5 PC6
## Age -0.41336263 -0.03629602
## Stage -0.21766761 0.18269976
## Tumor.Size -0.13361696 0.13694401
## Regional.Node.Examined -0.03947383 0.57624593
## Reginol.Node.Positive 0.10540722 -0.76394463
## Survival.Months -0.63971799 -0.15748760
## Sex 0.58479969 0.07795267
# Multiplying each column of the eigenvector’s matrix by the square-root of the corresponding eigenvalue in order to get the factor loadings
unrot.fact.emp <- sweep(pcafactors.emp,MARGIN=2,Cancer_pca$sdev[1:6],`*`)
unrot.fact.emp
## PC1 PC2 PC3 PC4
## Age -0.3219381 0.2217210 0.028087086 0.83377290
## Stage 0.8392786 -0.3660544 0.011661611 0.11595719
## Tumor.Size 0.8675206 -0.3184890 -0.007510772 0.15484336
## Regional.Node.Examined 0.3582368 0.7582769 0.339441563 -0.10801524
## Reginol.Node.Positive 0.6859789 0.4282840 0.196901988 0.03179084
## Survival.Months -0.2698113 -0.2060025 0.637460570 -0.32339272
## Sex -0.1115719 -0.3036565 0.707223528 0.30110393
## PC5 PC6
## Age -0.38801831 -0.02584919
## Stage -0.20432186 0.13011455
## Tumor.Size -0.12542456 0.09752836
## Regional.Node.Examined -0.03705358 0.41038905
## Reginol.Node.Positive 0.09894443 -0.54406372
## Survival.Months -0.60049525 -0.11215904
## Sex 0.54894413 0.05551609
# Computing communalities
communalities.emp <- rowSums(unrot.fact.emp^2)
communalities.emp
## Age Stage Tumor.Size
## 0.9999968 0.9106437 0.9033031
## Regional.Node.Examined Reginol.Node.Positive Survival.Months
## 0.9999975 0.9995706 0.9993482
## Sex
## 0.9999059
# Performing the varimax rotation. The default in the varimax function is norm=TRUE thus, Kaiser normalization is carried out
rot.fact.emp <- varimax(unrot.fact.emp)
#View(unrot.fact.emp)
rot.fact.emp
## $loadings
##
## Loadings:
## PC1 PC2 PC3 PC4 PC5 PC6
## Age -0.107 0.993
## Stage 0.945 -0.105
## Tumor.Size 0.928 -0.167
## Regional.Node.Examined 0.980 -0.194
## Reginol.Node.Positive 0.239 0.220 -0.941
## Survival.Months -0.994
## Sex 0.998
##
## PC1 PC2 PC3 PC4 PC5 PC6
## SS loadings 1.830 1.011 1.000 0.999 1.004 0.969
## Proportion Var 0.261 0.144 0.143 0.143 0.143 0.138
## Cumulative Var 0.261 0.406 0.549 0.691 0.835 0.973
##
## $rotmat
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.814726239 0.24618023 -0.07457614 -0.21390663 0.1823229 -0.43710088
## [2,] -0.439958445 0.70276665 -0.28025689 0.20217479 0.1924468 -0.39509654
## [3,] 0.005969577 0.33231165 0.68621305 0.02673842 -0.6180267 -0.18966543
## [4,] 0.195844185 -0.11019603 0.31084616 0.86017751 0.3346397 -0.03142433
## [5,] -0.245524198 -0.03787138 0.58518604 -0.41424811 0.6422905 -0.10817742
## [6,] 0.209726035 0.56701489 0.07705898 -0.03387497 0.1524624 0.77728935
# The print method of varimax omits loadings less than abs(0.1). In order to display all the loadings, it is necessary to ask explicitly the contents of the object $loadings
fact.load.emp <- rot.fact.emp$loadings[,1:6]
fact.load.emp
## PC1 PC2 PC3 PC4
## Age -0.10653554 -0.005943569 0.011264086 0.993246278
## Stage 0.94506454 0.021975085 -0.025493504 -0.073246335
## Tumor.Size 0.92844301 0.030233975 0.001659601 -0.068313774
## Regional.Node.Examined 0.03429352 0.979885765 -0.029934222 -0.005713421
## Reginol.Node.Positive 0.23946175 0.219548327 -0.010212504 -0.050094005
## Survival.Months -0.06480554 -0.004576002 0.054719191 0.007488852
## Sex -0.01724897 -0.028339093 0.997837889 0.011107489
## PC5 PC6
## Age -0.007533772 0.043472853
## Stage 0.002773981 -0.104838608
## Tumor.Size 0.087645663 -0.167425560
## Regional.Node.Examined 0.004082260 -0.194164824
## Reginol.Node.Positive 0.077041096 -0.940998477
## Survival.Months -0.993817418 0.066363802
## Sex -0.054055839 0.008912666
# Computing the rotated factor scores for the 30 European Countries. Notice that signs are reversed for factors F2 (PC2), F3 (PC3) and F4 (PC4)
scale.emp <- scale(Cancer[-1])
scale.emp
## Age Stage Tumor.Size Regional.Node.Examined
## [1,] 1.49983377 -1.0393086 -1.16262136 1.21298312
## [2,] -0.46330245 0.2231849 0.10298027 -0.03829778
## [3,] 0.40920254 1.4856783 1.24610431 -0.03829778
## [4,] 0.40920254 -1.0393086 -0.59105933 -1.53983486
## [5,] -0.79049182 0.2231849 0.34793542 -1.41470677
## [6,] -0.35423933 -1.0393086 -0.50940762 0.46221458
## [7,] -0.35423933 -1.0393086 -0.99931792 -0.41368205
## [8,] -1.55393369 0.2231849 -0.10114903 -0.66393823
## [9,] -1.55393369 2.7481718 2.87913866 0.71247076
## [10,] 1.60889690 2.7481718 -0.01949731 0.83759885
## [11,] 1.49983377 -1.0393086 -0.79518863 -0.66393823
## [12,] -0.89955495 1.4856783 1.08280088 -0.41368205
## [13,] 1.17264440 0.2231849 0.10298027 -0.16342587
## [14,] -0.68142870 -1.0393086 -0.71353691 1.08785503
## [15,] 0.84545503 0.2231849 0.10298027 0.21195840
## [16,] 0.73639191 -1.0393086 -0.55023347 0.71247076
## [17,] 0.19107629 0.2231849 0.55206471 -1.66496295
## [18,] -1.22674432 0.2231849 -0.34610418 0.96272694
## [19,] -0.68142870 0.2231849 -0.30527832 0.21195840
## [20,] 0.62732878 0.2231849 -0.14197489 0.71247076
## [21,] -0.68142870 0.2231849 -0.10114903 0.08683031
## [22,] 0.30013941 0.2231849 0.30710956 0.08683031
## [23,] 0.08201317 0.2231849 -0.14197489 -1.28957868
## [24,] -0.68142870 1.4856783 1.53188532 0.46221458
## [25,] 0.84545503 -1.0393086 -0.50940762 1.46323930
## [26,] 0.95451816 0.2231849 -0.42775590 2.08887975
## [27,] -0.68142870 0.2231849 0.71536815 1.33811121
## [28,] -0.89955495 -1.0393086 -0.63188519 -0.03829778
## [29,] 0.30013941 0.2231849 -0.30527832 -0.03829778
## [30,] 1.28170753 0.2231849 -0.46858176 -0.53881014
## [31,] -0.79049182 0.2231849 0.30710956 -1.41470677
## [32,] -0.13611308 -1.0393086 -0.71353691 -1.16445059
## [33,] 0.51826566 -1.0393086 -0.71353691 -1.03932250
## [34,] 0.62732878 -1.0393086 -0.50940762 0.58734267
## [35,] -0.89955495 0.2231849 -0.10114903 0.58734267
## [36,] -0.35423933 -1.0393086 -0.91766620 -0.66393823
## [37,] -0.02704996 0.2231849 -0.22362660 0.83759885
## [38,] -0.35423933 -1.0393086 -0.59105933 -0.03829778
## [39,] -0.57236557 0.2231849 0.10298027 -0.53881014
## [40,] -0.35423933 0.2231849 -0.38693004 0.08683031
## [41,] 0.30013941 1.4856783 1.53188532 -0.28855396
## [42,] 1.06358128 -1.0393086 -0.63188519 -0.28855396
## [43,] 0.84545503 0.2231849 -0.46858176 -1.53983486
## [44,] -0.13611308 0.2231849 -0.38693004 0.08683031
## [45,] 0.08201317 -1.0393086 -1.12179550 -0.41368205
## [46,] 1.28170753 1.4856783 0.75619401 -0.53881014
## [47,] -1.33580744 -1.0393086 -0.95849206 0.08683031
## [48,] 0.84545503 -1.0393086 -0.71353691 -0.28855396
## [49,] -0.13611308 0.2231849 -0.01949731 0.21195840
## [50,] 1.60889690 -1.0393086 -1.12179550 -0.78906632
## [51,] -1.88112306 0.2231849 -0.38693004 0.33708649
## [52,] 1.60889690 1.4856783 0.91949744 -0.66393823
## [53,] 0.62732878 1.4856783 3.57317826 -0.91419441
## [54,] 0.95451816 1.4856783 1.81766633 0.71247076
## [55,] 0.30013941 -1.0393086 -1.24427307 0.21195840
## [56,] 0.08201317 -1.0393086 -0.87684034 -0.16342587
## [57,] 0.84545503 0.2231849 -0.30527832 0.58734267
## [58,] -0.46330245 -1.0393086 -0.59105933 4.34118537
## [59,] -0.46330245 -1.0393086 -0.71353691 0.08683031
## [60,] 0.08201317 -1.0393086 -0.83601449 0.33708649
## [61,] 0.19107629 -1.0393086 -0.59105933 1.21298312
## [62,] -0.35423933 -1.0393086 -0.63188519 -0.28855396
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## [67,] -2.53550180 1.4856783 1.53188532 1.08785503
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## [74,] 1.28170753 -1.0393086 -0.91766620 0.08683031
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## [92,] -2.31737555 -1.0393086 -0.75436277 0.08683031
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## [102,] -0.79049182 -1.0393086 -0.67271105 1.33811121
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## [104,] 0.30013941 0.2231849 -0.22362660 -0.91419441
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## [106,] 0.62732878 0.2231849 -0.30527832 -1.53983486
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## [108,] 1.49983377 -1.0393086 -0.50940762 -0.28855396
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## [110,] 0.95451816 0.2231849 0.14380613 1.96375166
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## [117,] -0.46330245 1.4856783 1.77684048 -0.66393823
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## [120,] -0.13611308 0.2231849 -0.22362660 0.08683031
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## [123,] -0.46330245 0.2231849 0.71536815 0.21195840
## [124,] 0.51826566 0.2231849 0.22545784 1.08785503
## [125,] -0.13611308 -1.0393086 -0.71353691 1.08785503
## [126,] 0.84545503 -1.0393086 -0.63188519 0.21195840
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## [136,] -1.88112306 -1.0393086 -0.59105933 1.71349548
## [137,] -0.89955495 0.2231849 -0.30527832 -0.28855396
## [138,] 1.17264440 0.2231849 -0.46858176 0.71247076
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## [140,] -0.24517620 1.4856783 1.53188532 0.46221458
## [141,] -0.02704996 -1.0393086 -1.04014378 -1.28957868
## [142,] -1.99018618 -1.0393086 -0.55023347 -0.16342587
## [143,] -0.57236557 -1.0393086 -0.63188519 1.21298312
## [144,] 0.84545503 0.2231849 0.22545784 1.08785503
## [145,] -0.02704996 0.2231849 0.06215441 0.71247076
## [146,] 0.73639191 0.2231849 -0.10114903 0.08683031
## [147,] -0.89955495 -1.0393086 -1.16262136 0.46221458
## [148,] -1.77205993 1.4856783 1.61353704 -0.16342587
## [149,] 1.28170753 -1.0393086 -0.59105933 -1.66496295
## [150,] 0.51826566 0.2231849 -0.30527832 -0.16342587
## [151,] -1.77205993 -1.0393086 -0.95849206 0.46221458
## [152,] 1.39077065 0.2231849 -0.46858176 -0.03829778
## [153,] 0.62732878 -1.0393086 -0.50940762 0.08683031
## [154,] 0.73639191 -1.0393086 -0.71353691 -0.03829778
## [155,] 1.39077065 -1.0393086 -0.59105933 -0.03829778
## [156,] 1.60889690 1.4856783 2.75666109 0.21195840
## [157,] -0.79049182 -1.0393086 -0.63188519 0.08683031
## [158,] -1.66299681 -1.0393086 -1.04014378 -1.03932250
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## [160,] 0.08201317 0.2231849 0.42958714 -0.03829778
## [161,] 0.51826566 0.2231849 -0.10114903 0.46221458
## [162,] -0.13611308 -1.0393086 -1.04014378 -1.41470677
## [163,] 0.51826566 -1.0393086 -0.59105933 -1.53983486
## [164,] 0.30013941 -1.0393086 -0.83601449 0.71247076
## [165,] 0.73639191 0.2231849 -0.30527832 0.21195840
## [166,] 1.49983377 1.4856783 1.20527845 -1.41470677
## [167,] -0.02704996 -1.0393086 -0.50940762 -0.28855396
## [168,] -1.88112306 2.7481718 1.53188532 1.21298312
## [169,] -0.68142870 0.2231849 0.18463198 -0.78906632
## [170,] -0.13611308 -1.0393086 -0.79518863 -0.03829778
## [171,] 1.60889690 0.2231849 0.30710956 0.71247076
## [172,] 0.95451816 1.4856783 1.53188532 -0.41368205
## [173,] -0.57236557 -1.0393086 -0.83601449 -0.66393823
## [174,] 0.95451816 -1.0393086 -0.95849206 -0.66393823
## [175,] 0.62732878 -1.0393086 -0.91766620 1.21298312
## [176,] -1.44487056 1.4856783 0.91949744 -0.41368205
## [177,] 0.51826566 -1.0393086 -0.59105933 0.33708649
## [178,] -1.22674432 -1.0393086 -0.71353691 -0.91419441
## [179,] -0.24517620 0.2231849 -0.30527832 2.08887975
## [180,] 0.73639191 0.2231849 0.71536815 -0.41368205
## [181,] 0.62732878 -1.0393086 -0.91766620 2.21400784
## [182,] 0.73639191 0.2231849 -0.10114903 1.08785503
## [183,] 0.95451816 -1.0393086 -0.79518863 -1.41470677
## [184,] -0.68142870 0.2231849 0.30710956 0.08683031
## [185,] -0.35423933 1.4856783 2.75666109 -0.03829778
## [186,] 1.28170753 0.2231849 -0.30527832 -0.03829778
## [187,] 1.49983377 1.4856783 1.45023361 -1.41470677
## [188,] 0.40920254 0.2231849 -0.30527832 -0.03829778
## [189,] 0.84545503 0.2231849 -0.38693004 2.46426402
## [190,] -0.89955495 -1.0393086 -0.71353691 -0.03829778
## [191,] 0.40920254 0.2231849 -0.42775590 -0.28855396
## [192,] 0.62732878 -1.0393086 -1.04014378 -1.53983486
## [193,] 0.84545503 -1.0393086 -0.67271105 0.58734267
## [194,] -0.13611308 0.2231849 -0.34610418 -1.16445059
## [195,] -1.33580744 1.4856783 1.73601462 0.21195840
## [196,] 0.95451816 -1.0393086 -0.87684034 -1.16445059
## [197,] 0.08201317 0.2231849 0.10298027 0.21195840
## [198,] -0.46330245 1.4856783 1.12362674 -0.53881014
## [199,] -0.24517620 0.2231849 -0.10114903 0.96272694
## [200,] -0.79049182 0.2231849 -0.30527832 -0.41368205
## [201,] 0.08201317 0.2231849 -0.30527832 -0.03829778
## [202,] 0.62732878 0.2231849 -0.30527832 0.21195840
## [203,] 1.28170753 -1.0393086 -0.83601449 -1.66496295
## [204,] -0.46330245 0.2231849 -0.30527832 0.33708649
## [205,] 1.06358128 -1.0393086 -0.63188519 -1.53983486
## [206,] 1.39077065 -1.0393086 -0.87684034 -1.03932250
## [207,] 0.19107629 0.2231849 -0.01949731 1.21298312
## [208,] 0.62732878 0.2231849 -0.46858176 0.46221458
## [209,] 0.19107629 0.2231849 -0.30527832 -0.28855396
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## [211,] -1.11768119 1.4856783 1.73601462 -0.41368205
## [212,] -1.88112306 1.4856783 0.79701987 0.33708649
## [213,] -0.24517620 -1.0393086 -0.95849206 0.46221458
## [214,] 0.95451816 -1.0393086 -0.63188519 -0.66393823
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## [216,] 0.95451816 1.4856783 2.14427320 -1.28957868
## [217,] -1.11768119 0.2231849 0.71536815 -0.28855396
## [218,] 1.49983377 1.4856783 0.75619401 0.33708649
## [219,] 1.06358128 -1.0393086 -0.59105933 -1.28957868
## [220,] -0.46330245 1.4856783 1.73601462 1.58836739
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## [222,] 1.28170753 0.2231849 0.10298027 0.71247076
## [223,] -0.89955495 -1.0393086 -0.83601449 0.46221458
## [224,] -1.22674432 0.2231849 -0.38693004 -0.66393823
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## [226,] -1.22674432 -1.0393086 -0.67271105 1.58836739
## [227,] 0.51826566 1.4856783 1.00114916 0.71247076
## [228,] 0.08201317 1.4856783 0.71536815 3.46528874
## [229,] 0.73639191 -1.0393086 -0.63188519 -0.66393823
## [230,] 1.28170753 0.2231849 -0.01949731 0.08683031
## [231,] 0.08201317 0.2231849 -0.46858176 0.58734267
## [232,] 1.17264440 -1.0393086 -0.87684034 -0.91419441
## [233,] 1.60889690 0.2231849 0.30710956 0.96272694
## [234,] 0.51826566 -1.0393086 -0.71353691 -1.53983486
## [235,] 0.95451816 -1.0393086 -0.63188519 0.08683031
## [236,] 1.49983377 -1.0393086 -0.75436277 1.46323930
## [237,] -0.68142870 1.4856783 1.12362674 1.46323930
## [238,] 0.73639191 1.4856783 0.91949744 -0.28855396
## [239,] -1.22674432 2.7481718 3.57317826 1.71349548
## [240,] -1.11768119 -1.0393086 -0.87684034 -0.78906632
## [241,] -0.79049182 0.2231849 0.26628370 1.83862357
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## [243,] 1.60889690 0.2231849 -0.18280074 -0.66393823
## [244,] -1.66299681 0.2231849 0.18463198 0.46221458
## [245,] -1.22674432 0.2231849 0.30710956 0.08683031
## [246,] 1.06358128 -1.0393086 -0.95849206 0.46221458
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## [249,] -1.88112306 -1.0393086 -0.71353691 0.08683031
## [250,] -0.46330245 -1.0393086 -0.63188519 -0.41368205
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## [253,] -1.44487056 0.2231849 -0.10114903 -1.53983486
## [254,] -2.42643868 1.4856783 1.45023361 -0.16342587
## [255,] 1.17264440 1.4856783 3.16491967 0.58734267
## [256,] 1.39077065 0.2231849 -0.38693004 0.71247076
## [257,] 0.30013941 -1.0393086 -0.83601449 -0.16342587
## [258,] 0.95451816 -1.0393086 -0.79518863 -0.91419441
## [259,] -1.33580744 0.2231849 0.30710956 0.71247076
## [260,] 0.30013941 0.2231849 -0.10114903 -0.28855396
## [261,] -1.33580744 -1.0393086 -0.95849206 -0.41368205
## [262,] -0.89955495 0.2231849 -0.42775590 -0.66393823
## [263,] -0.79049182 0.2231849 -0.10114903 -0.66393823
## [264,] 1.39077065 -1.0393086 -0.83601449 -1.41470677
## [265,] 1.39077065 -1.0393086 -0.91766620 2.33913593
## [266,] 1.17264440 0.2231849 -0.30527832 -1.41470677
## [267,] 1.17264440 -1.0393086 -0.67271105 2.33913593
## [268,] -2.31737555 1.4856783 1.32775603 -1.41470677
## [269,] 1.06358128 0.2231849 -0.42775590 -1.28957868
## [270,] 1.28170753 -1.0393086 -0.63188519 0.71247076
## [271,] -2.20831243 1.4856783 1.12362674 -0.16342587
## [272,] 0.08201317 0.2231849 -0.42775590 0.71247076
## [273,] -0.79049182 0.2231849 0.10298027 0.46221458
## [274,] 0.40920254 -1.0393086 -0.59105933 -0.66393823
## [275,] -1.77205993 0.2231849 0.06215441 -0.41368205
## [276,] 0.30013941 -1.0393086 -1.08096964 -1.53983486
## [277,] 1.17264440 1.4856783 2.96079038 -1.28957868
## [278,] -0.24517620 1.4856783 2.75666109 1.08785503
## [279,] 1.39077065 -1.0393086 -0.50940762 -0.03829778
## [280,] 0.30013941 1.4856783 1.00114916 -0.03829778
## [281,] 0.73639191 -1.0393086 -0.91766620 0.21195840
## [282,] -1.00861807 -1.0393086 -0.63188519 -0.28855396
## [283,] -0.46330245 0.2231849 -0.30527832 0.46221458
## [284,] -0.46330245 0.2231849 -0.46858176 -0.28855396
## [285,] -0.13611308 0.2231849 0.51123885 -0.03829778
## [286,] -0.02704996 0.2231849 0.71536815 -0.91419441
## [287,] 0.40920254 0.2231849 0.10298027 -0.16342587
## [288,] 0.19107629 0.2231849 0.22545784 -0.28855396
## [289,] 1.49983377 -1.0393086 -0.67271105 1.96375166
## [290,] -1.44487056 1.4856783 4.38969544 3.34016065
## [291,] 0.73639191 0.2231849 -0.30527832 3.08990447
## [292,] 1.17264440 -1.0393086 -0.59105933 0.33708649
## [293,] 1.60889690 -1.0393086 -0.59105933 -0.41368205
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## [298,] 1.17264440 0.2231849 -0.14197489 -0.41368205
## [299,] -0.13611308 -1.0393086 -0.91766620 0.83759885
## [300,] 1.39077065 1.4856783 1.20527845 -0.16342587
## [301,] -1.22674432 0.2231849 0.71536815 0.46221458
## [302,] -0.79049182 0.2231849 -0.14197489 1.08785503
## [303,] -0.68142870 -1.0393086 -0.71353691 1.96375166
## [304,] 0.84545503 -1.0393086 -0.71353691 3.96580110
## [305,] 1.49983377 0.2231849 0.38876128 1.33811121
## [306,] 0.30013941 1.4856783 3.98143685 -0.53881014
## [307,] -1.55393369 0.2231849 -0.46858176 0.96272694
## [308,] 0.19107629 1.4856783 0.75619401 -0.53881014
## [309,] -0.24517620 0.2231849 -0.10114903 -1.28957868
## [310,] -1.55393369 0.2231849 0.10298027 0.58734267
## [311,] -0.35423933 0.2231849 -0.06032317 -1.28957868
## [312,] 1.39077065 -1.0393086 -0.75436277 0.08683031
## [313,] -0.02704996 -1.0393086 -0.71353691 -0.03829778
## [314,] 0.19107629 1.4856783 1.12362674 1.58836739
## [315,] -0.68142870 -1.0393086 -0.50940762 -0.28855396
## [316,] 0.30013941 0.2231849 -0.42775590 -1.28957868
## [317,] -0.79049182 1.4856783 1.94014391 -0.03829778
## [318,] -0.02704996 -1.0393086 -0.71353691 -0.03829778
## [319,] -1.44487056 1.4856783 2.75666109 1.71349548
## [320,] 1.17264440 0.2231849 -0.10114903 -0.28855396
## [321,] 0.40920254 -1.0393086 -0.99931792 0.46221458
## [322,] -1.77205993 -1.0393086 -0.71353691 0.08683031
## [323,] -1.77205993 1.4856783 1.94014391 -0.78906632
## [324,] 0.62732878 0.2231849 -0.10114903 0.58734267
## [325,] 0.40920254 0.2231849 -0.30527832 0.21195840
## [326,] 0.95451816 0.2231849 -0.34610418 0.08683031
## [327,] -0.13611308 0.2231849 0.10298027 -0.03829778
## [328,] -1.22674432 -1.0393086 -0.83601449 -1.66496295
## [329,] 0.62732878 2.7481718 0.51123885 -0.66393823
## [330,] 0.62732878 0.2231849 -0.30527832 -0.53881014
## [331,] -0.79049182 0.2231849 0.10298027 1.21298312
## [332,] -0.68142870 0.2231849 -0.18280074 0.58734267
## [333,] 0.51826566 -1.0393086 -0.63188519 -1.03932250
## [334,] 0.19107629 -1.0393086 -0.71353691 0.58734267
## [335,] -0.13611308 0.2231849 -0.01949731 -0.16342587
## [336,] -0.68142870 -1.0393086 -0.71353691 -0.41368205
## [337,] -0.24517620 1.4856783 1.12362674 -1.28957868
## [338,] 0.73639191 1.4856783 2.34840250 -0.16342587
## [339,] 1.28170753 -1.0393086 -0.87684034 0.58734267
## [340,] -1.00861807 0.2231849 0.18463198 -0.16342587
## [341,] -0.24517620 0.2231849 -0.46858176 -0.28855396
## [342,] 1.39077065 -1.0393086 -1.24427307 0.58734267
## [343,] -1.55393369 1.4856783 1.53188532 0.33708649
## [344,] -0.46330245 -1.0393086 -0.99931792 -0.66393823
## [345,] 1.17264440 0.2231849 -0.42775590 1.08785503
## [346,] 0.08201317 0.2231849 0.30710956 -0.28855396
## [347,] -0.79049182 -1.0393086 -0.79518863 -1.16445059
## [348,] -0.57236557 0.2231849 -0.01949731 0.21195840
## [349,] -0.13611308 -1.0393086 -1.12179550 1.83862357
## [350,] -0.13611308 -1.0393086 -0.59105933 0.33708649
## [351,] -1.11768119 1.4856783 0.79701987 1.21298312
## [352,] -0.02704996 0.2231849 -0.06032317 0.21195840
## [353,] -0.35423933 -1.0393086 -0.75436277 -1.03932250
## [354,] -0.89955495 -1.0393086 -1.04014378 -0.91419441
## [355,] -0.79049182 -1.0393086 -0.83601449 -1.66496295
## [356,] 1.49983377 0.2231849 -0.46858176 0.46221458
## [357,] -0.46330245 -1.0393086 -0.50940762 1.08785503
## [358,] 1.39077065 0.2231849 -0.26445246 -1.16445059
## [359,] -0.79049182 -1.0393086 -0.67271105 -1.41470677
## [360,] 1.49983377 -1.0393086 -0.71353691 0.71247076
## [361,] 0.08201317 0.2231849 -0.30527832 -0.53881014
## [362,] -0.79049182 -1.0393086 -0.50940762 1.08785503
## [363,] 0.19107629 1.4856783 1.94014391 1.21298312
## [364,] -0.35423933 0.2231849 -0.10114903 -1.53983486
## [365,] -1.44487056 -1.0393086 -0.67271105 -0.41368205
## [366,] 1.39077065 -1.0393086 -0.50940762 0.21195840
## [367,] 0.40920254 -1.0393086 -0.63188519 0.58734267
## [368,] 1.39077065 1.4856783 2.75666109 1.33811121
## [369,] 0.95451816 0.2231849 0.34793542 -0.03829778
## [370,] 1.60889690 -1.0393086 -0.67271105 -0.28855396
## [371,] 0.51826566 0.2231849 -0.30527832 1.96375166
## [372,] -1.11768119 2.7481718 3.08326796 0.21195840
## [373,] 1.17264440 -1.0393086 -0.83601449 -1.53983486
## [374,] -0.68142870 0.2231849 0.22545784 1.21298312
## [375,] -1.66299681 0.2231849 -0.34610418 1.46323930
## [376,] 0.08201317 0.2231849 0.51123885 -0.03829778
## [377,] -0.46330245 1.4856783 2.67500937 -0.03829778
## [378,] -1.66299681 0.2231849 -0.30527832 0.21195840
## [379,] -0.57236557 0.2231849 -0.10114903 0.46221458
## Reginol.Node.Positive Survival.Months Sex
## [1,] -0.62683648 -0.51850792 -0.5329113
## [2,] 0.16309212 -0.42922373 -0.5329113
## [3,] 0.55805642 0.15112350 -0.5329113
## [4,] -0.62683648 0.55290236 -0.5329113
## [5,] -0.62683648 -0.96492887 -0.5329113
## [6,] -0.42935433 0.77611283 -0.5329113
## [7,] -0.62683648 -0.78636049 -0.5329113
## [8,] -0.62683648 -2.57204428 -0.5329113
## [9,] 2.73036007 -0.07208697 -0.5329113
## [10,] 1.54546717 0.91003912 -0.5329113
## [11,] -0.62683648 -0.33993954 -0.5329113
## [12,] -0.23187218 0.91003912 -0.5329113
## [13,] -0.23187218 -0.69707630 -0.5329113
## [14,] 0.55805642 -1.50063401 -0.5329113
## [15,] 1.94043147 -0.33993954 -0.5329113
## [16,] -0.62683648 -1.00957096 -0.5329113
## [17,] -0.62683648 1.49038635 -0.5329113
## [18,] -0.62683648 -0.42922373 -0.5329113
## [19,] -0.62683648 1.57967054 -0.5329113
## [20,] -0.62683648 0.24040769 -0.5329113
## [21,] -0.42935433 0.41897607 -0.5329113
## [22,] 0.16309212 -0.96492887 -0.5329113
## [23,] -0.62683648 0.28504979 -0.5329113
## [24,] -0.62683648 1.35646006 -0.5329113
## [25,] 3.52028867 1.17789169 -0.5329113
## [26,] 2.53287792 -0.07208697 -0.5329113
## [27,] 3.71777082 1.35646006 -0.5329113
## [28,] -0.62683648 0.46361817 -0.5329113
## [29,] -0.03439003 -0.33993954 -0.5329113
## [30,] -0.62683648 0.64218655 -0.5329113
## [31,] -0.62683648 -0.87564468 -0.5329113
## [32,] -0.62683648 -1.00957096 -0.5329113
## [33,] -0.62683648 0.82075493 -0.5329113
## [34,] -0.23187218 -0.42922373 -0.5329113
## [35,] 1.15050287 -1.81312867 -0.5329113
## [36,] -0.42935433 0.24040769 1.8715337
## [37,] 0.36057427 -1.54527610 1.8715337
## [38,] -0.42935433 1.40110216 1.8715337
## [39,] -0.42935433 0.46361817 1.8715337
## [40,] 0.16309212 1.49038635 1.8715337
## [41,] 1.54546717 -1.32206563 1.8715337
## [42,] -0.42935433 -0.47386582 1.8715337
## [43,] -0.62683648 0.64218655 1.8715337
## [44,] 0.36057427 0.55290236 1.8715337
## [45,] -0.42935433 -0.38458164 1.8715337
## [46,] 0.16309212 0.82075493 1.8715337
## [47,] -0.42935433 -1.45599191 1.8715337
## [48,] -0.62683648 -0.56315001 1.8715337
## [49,] 0.95302072 0.46361817 1.8715337
## [50,] -0.23187218 0.46361817 1.8715337
## [51,] -0.23187218 -0.02744488 1.8715337
## [52,] -0.62683648 -0.02744488 1.8715337
## [53,] -0.62683648 0.64218655 1.8715337
## [54,] -0.42935433 -0.07208697 1.8715337
## [55,] -0.62683648 0.10648141 1.8715337
## [56,] -0.62683648 0.06183931 1.8715337
## [57,] -0.62683648 0.86539702 -0.5329113
## [58,] -0.62683648 1.53502844 -0.5329113
## [59,] -0.62683648 0.06183931 -0.5329113
## [60,] -0.42935433 0.24040769 -0.5329113
## [61,] -0.42935433 0.37433398 -0.5329113
## [62,] -0.62683648 -1.00957096 -0.5329113
## [63,] -0.62683648 0.28504979 -0.5329113
## [64,] -0.42935433 0.15112350 -0.5329113
## [65,] -0.23187218 -0.51850792 -0.5329113
## [66,] -0.62683648 1.53502844 -0.5329113
## [67,] 3.71777082 -1.23278144 -0.5329113
## [68,] -0.23187218 0.59754445 -0.5329113
## [69,] -0.62683648 0.32969188 -0.5329113
## [70,] -0.23187218 0.55290236 -0.5329113
## [71,] 0.75553857 1.44574425 -0.5329113
## [72,] 3.12532437 -2.66132847 -0.5329113
## [73,] -0.62683648 -0.87564468 -0.5329113
## [74,] -0.62683648 1.17789169 -0.5329113
## [75,] 2.33539577 0.59754445 -0.5329113
## [76,] -0.62683648 1.04396540 -0.5329113
## [77,] -0.03439003 0.32969188 1.8715337
## [78,] -0.62683648 1.53502844 1.8715337
## [79,] -0.62683648 0.41897607 1.8715337
## [80,] -0.62683648 -0.74171839 1.8715337
## [81,] 1.74294932 1.31181797 1.8715337
## [82,] -0.62683648 -0.29529745 1.8715337
## [83,] -0.42935433 0.01719722 1.8715337
## [84,] -0.62683648 -0.74171839 1.8715337
## [85,] -0.62683648 -0.29529745 1.8715337
## [86,] 1.34798502 -0.02744488 1.8715337
## [87,] 0.16309212 0.46361817 1.8715337
## [88,] -0.62683648 0.55290236 1.8715337
## [89,] -0.62683648 1.04396540 1.8715337
## [90,] -0.62683648 1.04396540 1.8715337
## [91,] -0.62683648 0.86539702 1.8715337
## [92,] -0.62683648 -0.65243420 1.8715337
## [93,] -0.03439003 0.68682864 1.8715337
## [94,] 2.33539577 -1.41134982 1.8715337
## [95,] -0.23187218 0.86539702 1.8715337
## [96,] -0.42935433 -0.96492887 1.8715337
## [97,] -0.42935433 -2.08098124 1.8715337
## [98,] -0.62683648 0.06183931 1.8715337
## [99,] -0.23187218 -0.38458164 -0.5329113
## [100,] -0.62683648 -0.96492887 -0.5329113
## [101,] 3.91525297 -0.78636049 -0.5329113
## [102,] -0.62683648 0.06183931 -0.5329113
## [103,] -0.62683648 -2.83989685 -0.5329113
## [104,] -0.62683648 -0.83100258 -0.5329113
## [105,] -0.23187218 -0.29529745 -0.5329113
## [106,] -0.62683648 -0.60779211 -0.5329113
## [107,] -0.62683648 -2.12562333 -0.5329113
## [108,] -0.42935433 -0.33993954 -0.5329113
## [109,] -0.42935433 1.53502844 -0.5329113
## [110,] -0.23187218 -0.47386582 -0.5329113
## [111,] -0.03439003 -0.25065535 -0.5329113
## [112,] -0.23187218 0.32969188 -0.5329113
## [113,] 1.15050287 0.10648141 -0.5329113
## [114,] -0.42935433 -0.11672907 -0.5329113
## [115,] 0.16309212 1.40110216 -0.5329113
## [116,] -0.23187218 -0.87564468 -0.5329113
## [117,] -0.62683648 0.95468121 -0.5329113
## [118,] 0.95302072 0.99932331 -0.5329113
## [119,] -0.23187218 0.86539702 -0.5329113
## [120,] -0.42935433 -0.65243420 -0.5329113
## [121,] -0.42935433 0.99932331 -0.5329113
## [122,] -0.23187218 0.32969188 -0.5329113
## [123,] 2.33539577 -0.42922373 -0.5329113
## [124,] -0.03439003 0.64218655 -0.5329113
## [125,] -0.42935433 -1.00957096 -0.5329113
## [126,] -0.62683648 -2.57204428 -0.5329113
## [127,] -0.42935433 1.26717587 -0.5329113
## [128,] -0.62683648 -0.96492887 -0.5329113
## [129,] -0.42935433 0.32969188 -0.5329113
## [130,] -0.23187218 0.24040769 -0.5329113
## [131,] -0.62683648 -0.96492887 -0.5329113
## [132,] 0.36057427 0.06183931 -0.5329113
## [133,] -0.62683648 1.08860750 -0.5329113
## [134,] -0.62683648 0.68682864 -0.5329113
## [135,] 0.55805642 -1.36670772 -0.5329113
## [136,] 0.16309212 -0.78636049 -0.5329113
## [137,] -0.62683648 0.55290236 -0.5329113
## [138,] -0.62683648 -0.20601326 -0.5329113
## [139,] 1.15050287 -0.83100258 -0.5329113
## [140,] 0.95302072 1.44574425 -0.5329113
## [141,] -0.62683648 0.64218655 -0.5329113
## [142,] -0.03439003 1.35646006 -0.5329113
## [143,] -0.62683648 -0.96492887 -0.5329113
## [144,] -0.23187218 -1.32206563 -0.5329113
## [145,] -0.62683648 -0.87564468 -0.5329113
## [146,] -0.62683648 1.57967054 -0.5329113
## [147,] -0.42935433 0.91003912 -0.5329113
## [148,] 0.75553857 -0.87564468 -0.5329113
## [149,] -0.62683648 -0.11672907 -0.5329113
## [150,] -0.23187218 0.46361817 -0.5329113
## [151,] -0.62683648 1.31181797 -0.5329113
## [152,] -0.42935433 -0.33993954 -0.5329113
## [153,] -0.62683648 -0.74171839 -0.5329113
## [154,] 0.16309212 1.17789169 -0.5329113
## [155,] -0.42935433 -0.69707630 -0.5329113
## [156,] 0.36057427 0.86539702 -0.5329113
## [157,] -0.62683648 -0.92028677 -0.5329113
## [158,] -0.62683648 1.35646006 -0.5329113
## [159,] -0.62683648 -0.02744488 -0.5329113
## [160,] 1.94043147 -2.61668638 -0.5329113
## [161,] -0.03439003 -2.70597057 -0.5329113
## [162,] -0.62683648 -0.83100258 -0.5329113
## [163,] -0.62683648 0.46361817 -0.5329113
## [164,] -0.42935433 0.77611283 -0.5329113
## [165,] 0.36057427 -0.69707630 -0.5329113
## [166,] -0.62683648 -0.78636049 -0.5329113
## [167,] 0.55805642 0.01719722 -0.5329113
## [168,] 2.53287792 1.35646006 -0.5329113
## [169,] -0.62683648 -0.92028677 -0.5329113
## [170,] -0.62683648 1.26717587 -0.5329113
## [171,] -0.42935433 -0.42922373 -0.5329113
## [172,] -0.23187218 0.06183931 -0.5329113
## [173,] -0.42935433 0.55290236 -0.5329113
## [174,] -0.62683648 0.68682864 -0.5329113
## [175,] -0.42935433 1.08860750 -0.5329113
## [176,] -0.62683648 0.10648141 -0.5329113
## [177,] 1.15050287 -1.09885515 -0.5329113
## [178,] -0.42935433 0.24040769 -0.5329113
## [179,] 1.94043147 -0.74171839 -0.5329113
## [180,] 0.16309212 -0.33993954 -0.5329113
## [181,] -0.62683648 0.95468121 -0.5329113
## [182,] -0.42935433 0.10648141 -0.5329113
## [183,] -0.62683648 -2.17026543 -0.5329113
## [184,] 1.74294932 -0.51850792 -0.5329113
## [185,] 1.34798502 0.59754445 -0.5329113
## [186,] -0.42935433 0.64218655 -0.5329113
## [187,] -0.23187218 0.41897607 -0.5329113
## [188,] -0.42935433 -0.02744488 -0.5329113
## [189,] 0.95302072 0.82075493 -0.5329113
## [190,] -0.62683648 0.32969188 -0.5329113
## [191,] -0.62683648 -0.51850792 -0.5329113
## [192,] -0.62683648 0.77611283 -0.5329113
## [193,] -0.03439003 -0.25065535 -0.5329113
## [194,] -0.62683648 0.55290236 -0.5329113
## [195,] 1.74294932 -0.74171839 -0.5329113
## [196,] -0.62683648 -0.96492887 -0.5329113
## [197,] -0.42935433 -0.74171839 -0.5329113
## [198,] 0.16309212 1.17789169 -0.5329113
## [199,] -0.42935433 -0.83100258 -0.5329113
## [200,] -0.42935433 1.40110216 -0.5329113
## [201,] -0.42935433 0.24040769 -0.5329113
## [202,] -0.03439003 -0.38458164 -0.5329113
## [203,] -0.62683648 -1.18813934 -0.5329113
## [204,] 1.54546717 -2.08098124 -0.5329113
## [205,] -0.62683648 -0.16137116 -0.5329113
## [206,] -0.62683648 -0.83100258 -0.5329113
## [207,] -0.62683648 0.86539702 -0.5329113
## [208,] -0.62683648 1.49038635 -0.5329113
## [209,] -0.62683648 0.19576560 -0.5329113
## [210,] -0.62683648 0.99932331 -0.5329113
## [211,] -0.03439003 -0.02744488 -0.5329113
## [212,] 1.54546717 -2.52740219 -0.5329113
## [213,] 2.53287792 1.53502844 -0.5329113
## [214,] -0.62683648 -0.69707630 -0.5329113
## [215,] 0.95302072 -0.69707630 -0.5329113
## [216,] -0.03439003 -2.48276009 -0.5329113
## [217,] -0.62683648 -1.81312867 -0.5329113
## [218,] -0.62683648 0.59754445 -0.5329113
## [219,] -0.42935433 -0.42922373 -0.5329113
## [220,] 4.50769942 -2.17026543 -0.5329113
## [221,] 1.74294932 -2.12562333 -0.5329113
## [222,] 0.55805642 -0.96492887 -0.5329113
## [223,] -0.42935433 1.57967054 -0.5329113
## [224,] -0.23187218 0.19576560 -0.5329113
## [225,] -0.62683648 0.68682864 -0.5329113
## [226,] -0.42935433 1.31181797 -0.5329113
## [227,] 0.95302072 -0.51850792 -0.5329113
## [228,] -0.62683648 -0.25065535 -0.5329113
## [229,] -0.62683648 -0.83100258 -0.5329113
## [230,] -0.03439003 0.95468121 -0.5329113
## [231,] -0.62683648 0.82075493 -0.5329113
## [232,] 0.55805642 -0.56315001 -0.5329113
## [233,] 0.16309212 -0.60779211 -0.5329113
## [234,] -0.62683648 -0.16137116 -0.5329113
## [235,] -0.42935433 0.99932331 -0.5329113
## [236,] -0.62683648 0.01719722 -0.5329113
## [237,] 3.32280652 -0.83100258 -0.5329113
## [238,] -0.62683648 1.40110216 -0.5329113
## [239,] 4.31021727 -2.48276009 -0.5329113
## [240,] -0.42935433 0.24040769 -0.5329113
## [241,] -0.62683648 -1.00957096 -0.5329113
## [242,] -0.42935433 1.22253378 -0.5329113
## [243,] -0.42935433 1.57967054 -0.5329113
## [244,] 2.13791362 0.41897607 -0.5329113
## [245,] 0.16309212 0.68682864 -0.5329113
## [246,] -0.62683648 1.40110216 -0.5329113
## [247,] -0.62683648 1.08860750 -0.5329113
## [248,] -0.23187218 -1.41134982 -0.5329113
## [249,] -0.42935433 0.28504979 -0.5329113
## [250,] -0.62683648 0.91003912 -0.5329113
## [251,] 0.36057427 1.53502844 -0.5329113
## [252,] -0.62683648 -0.78636049 -0.5329113
## [253,] -0.42935433 0.59754445 -0.5329113
## [254,] 0.36057427 -0.11672907 -0.5329113
## [255,] -0.42935433 -0.92028677 -0.5329113
## [256,] -0.42935433 0.95468121 -0.5329113
## [257,] -0.42935433 0.19576560 -0.5329113
## [258,] -0.62683648 -0.60779211 -0.5329113
## [259,] -0.62683648 0.32969188 -0.5329113
## [260,] -0.62683648 -0.38458164 -0.5329113
## [261,] -0.42935433 -2.88453895 -0.5329113
## [262,] -0.62683648 1.44574425 -0.5329113
## [263,] -0.42935433 0.10648141 -0.5329113
## [264,] -0.23187218 -0.20601326 -0.5329113
## [265,] -0.62683648 1.17789169 -0.5329113
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## attr(,"scaled:center")
## Age Stage Tumor.Size
## 54.2480211 1.8232190 32.4775726
## Regional.Node.Examined Reginol.Node.Positive Survival.Months
## 14.3060686 4.1741425 71.6147757
## Sex
## 0.2216359
## attr(,"scaled:scale")
## Age Stage Tumor.Size
## 9.1690020 0.7920833 24.4942796
## Regional.Node.Examined Reginol.Node.Positive Survival.Months
## 7.9918106 5.0637488 22.4003825
## Sex
## 0.4158964
#Logistic Regression
library(readr)
library(ggplot2)
library(cowplot)
#library(regclass)
#library(caret)
library(e1071)
library(pROC)
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
data<- read_csv("~/Downloads/BC.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): Survivor, Age, Stage, Tumor.Size, Regional.Node.Examined, Reginol.N...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(data)
## # A tibble: 6 × 8
## Survivor Age Stage Tumor.Size Regional.Node.Examined Reginol…¹ Survi…² Sex
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 68 1 4 24 1 60 0
## 2 1 50 2 35 14 5 62 0
## 3 1 58 3 63 14 7 75 0
## 4 1 58 1 18 2 1 84 0
## 5 1 47 2 41 3 1 50 0
## 6 1 51 1 20 18 2 89 0
## # … with abbreviated variable names ¹​Reginol.Node.Positive, ²​Survival.Months
str(data)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Survivor : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## $ Age : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
## $ Stage : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
## $ Tumor.Size : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
## $ Regional.Node.Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
## $ Reginol.Node.Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
## $ Survival.Months : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
## $ Sex : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "spec")=
## .. cols(
## .. Survivor = col_double(),
## .. Age = col_double(),
## .. Stage = col_double(),
## .. Tumor.Size = col_double(),
## .. Regional.Node.Examined = col_double(),
## .. Reginol.Node.Positive = col_double(),
## .. Survival.Months = col_double(),
## .. Sex = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
## Exploratory Analysis
xtabs(~ Survivor + Age, data=data)
## Age
## Survivor 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## 0 1 0 0 1 0 3 2 0 1 1 1 1 2 2 0 1 1 0 5 1 1 1 3
## 1 1 1 2 0 1 3 5 6 6 4 5 10 3 5 12 15 15 6 13 11 12 18 8
## Age
## Survivor 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
## 0 3 2 3 0 1 1 3 3 3 2 1 2 3 1 3
## 1 13 9 9 11 12 14 11 7 11 4 12 11 15 12 7
xtabs(~ Survivor + Stage, data=data)
## Stage
## Survivor 1 2 3 4
## 0 12 28 16 3
## 1 136 132 45 7
xtabs(~ Survivor + Tumor.Size, data=data)
## Tumor.Size
## Survivor 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
## 0 0 0 0 0 0 0 0 1 0 0 2 3 0 0 1 1 3 0 1 1 1 1 1
## 1 2 1 2 3 1 5 4 5 7 7 10 4 5 26 8 16 12 5 14 10 8 7 5
## Tumor.Size
## Survivor 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 45 46 48 49 50
## 0 3 2 1 2 0 4 0 0 2 1 0 0 1 1 2 0 0 1 1 0 0 1 3
## 1 25 1 3 1 4 14 2 6 2 14 1 3 3 0 8 2 1 0 6 1 1 0 8
## Tumor.Size
## Survivor 51 52 55 57 59 60 62 63 65 68 70 72 75 76 77 80 85 90 98 100 103 105
## 0 1 1 0 0 0 3 0 0 0 0 3 2 1 0 0 1 1 0 0 1 0 0
## 1 4 1 4 2 1 3 2 1 2 2 5 0 3 1 1 3 0 1 1 4 1 1
## Tumor.Size
## Survivor 108 110 120 130 140
## 0 1 0 1 1 1
## 1 0 1 2 1 0
xtabs(~ Survivor + Regional.Node.Examined, data=data)
## Regional.Node.Examined
## Survivor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
## 0 1 1 4 3 2 0 2 2 2 1 3 3 2 3 2 3 3 2 1 4 1 0 4
## 1 6 13 10 8 8 8 8 7 19 13 15 22 15 29 21 18 7 16 14 13 4 4 7
## Regional.Node.Examined
## Survivor 24 25 26 27 28 29 30 31 32 33 34 39 41 42 46 49
## 0 2 0 0 2 2 1 0 0 0 1 1 0 1 0 0 0
## 1 9 4 4 1 1 1 5 2 1 2 1 1 0 1 1 1
xtabs(~ Survivor + Reginol.Node.Positive, data=data)
## Reginol.Node.Positive
## Survivor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## 0 15 7 7 2 2 2 2 1 2 4 0 3 1 2 1 1 2
## 1 135 64 31 19 13 10 6 2 9 3 4 3 5 4 1 2 3
## Reginol.Node.Positive
## Survivor 18 20 21 22 23 24 26 27 28
## 0 0 1 0 0 1 1 1 1 0
## 1 1 0 1 1 2 0 0 0 1
xtabs(~ Survivor + Survival.Months, data=data)
## Survival.Months
## Survivor 7 8 11 12 13 14 15 16 23 24 25 31 34 37 38 39 40 41 42 44 45 47 48 49
## 0 0 0 0 1 1 2 1 4 3 2 2 1 1 1 0 1 3 1 2 1 2 2 0 1
## 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 2 7
## Survival.Months
## Survivor 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## 0 2 1 2 2 3 1 0 0 0 0 1 0 1 1 2 0 0 2 0 0 0 1 0
## 1 9 3 3 9 3 6 6 8 4 5 6 6 5 5 4 5 3 2 6 3 4 6 4
## Survival.Months
## Survivor 73 74 75 76 77 78 79 80 81 82 84 85 86 87 88 89 90 91 92 93 94 95 96
## 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0
## 1 9 7 5 5 7 3 7 2 8 8 7 6 8 6 2 6 5 7 9 4 5 4 3
## Survival.Months
## Survivor 97 98 99 100 101 102 103 104 105 106 107
## 0 0 0 0 1 0 0 0 0 0 0 0
## 1 2 6 2 5 4 8 5 5 4 6 8
xtabs(~ Survivor + Sex, data=data)
## Sex
## Survivor 0 1
## 0 48 11
## 1 247 73
logistic_simple <- glm(Survivor ~ Sex, data=data, family="binomial")
summary(logistic_simple)
##
## Call:
## glm(formula = Survivor ~ Sex, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0164 0.5298 0.5960 0.5960 0.5960
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.6382 0.1577 10.385 <2e-16 ***
## Sex 0.2544 0.3598 0.707 0.48
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 327.78 on 378 degrees of freedom
## Residual deviance: 327.26 on 377 degrees of freedom
## AIC: 331.26
##
## Number of Fisher Scoring iterations: 4
# Inference
# Here the logistic regression model includes only one predictor variable, Sex. The estimated intercept is 1.6382 and the estimated coefficient for Sex is 0.2544. The p-value for Sex is 0.48, which indicates that the effect of Sex on Survivor is not statistically significant at the 0.05 level. Therefore, we cannot conclude that there is a significant association between Sex and Survivor in this model.
female.log.odds <- log(25 / 71)
female.log.odds
## [1] -1.043804
# Now you know how these are calculated
male.log.odds.ratio <- log((112 / 89) / (25/71))
male.log.odds.ratio
## [1] 1.273667
## Lastly, let's see what this logistic regression predicts, given
## that a patient is either female or male (and no other data about them).
predicted.data <- data.frame(probability.of.Survivor=logistic_simple$fitted.values,sex=data$Sex)
predicted.data
## probability.of.Survivor sex
## 1 0.8372881 0
## 2 0.8372881 0
## 3 0.8372881 0
## 4 0.8372881 0
## 5 0.8372881 0
## 6 0.8372881 0
## 7 0.8372881 0
## 8 0.8372881 0
## 9 0.8372881 0
## 10 0.8372881 0
## 11 0.8372881 0
## 12 0.8372881 0
## 13 0.8372881 0
## 14 0.8372881 0
## 15 0.8372881 0
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## 35 0.8372881 0
## 36 0.8690476 1
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## 232 0.8372881 0
## 233 0.8372881 0
## 234 0.8372881 0
## 235 0.8372881 0
## 236 0.8372881 0
## 237 0.8372881 0
## 238 0.8372881 0
## 239 0.8372881 0
## 240 0.8372881 0
## 241 0.8372881 0
## 242 0.8372881 0
## 243 0.8372881 0
## 244 0.8372881 0
## 245 0.8372881 0
## 246 0.8372881 0
## 247 0.8372881 0
## 248 0.8372881 0
## 249 0.8372881 0
## 250 0.8372881 0
## 251 0.8372881 0
## 252 0.8372881 0
## 253 0.8372881 0
## 254 0.8372881 0
## 255 0.8372881 0
## 256 0.8372881 0
## 257 0.8372881 0
## 258 0.8372881 0
## 259 0.8372881 0
## 260 0.8372881 0
## 261 0.8372881 0
## 262 0.8372881 0
## 263 0.8372881 0
## 264 0.8372881 0
## 265 0.8372881 0
## 266 0.8372881 0
## 267 0.8372881 0
## 268 0.8372881 0
## 269 0.8372881 0
## 270 0.8372881 0
## 271 0.8372881 0
## 272 0.8372881 0
## 273 0.8372881 0
## 274 0.8372881 0
## 275 0.8372881 0
## 276 0.8372881 0
## 277 0.8372881 0
## 278 0.8372881 0
## 279 0.8372881 0
## 280 0.8372881 0
## 281 0.8372881 0
## 282 0.8372881 0
## 283 0.8372881 0
## 284 0.8372881 0
## 285 0.8372881 0
## 286 0.8372881 0
## 287 0.8372881 0
## 288 0.8372881 0
## 289 0.8372881 0
## 290 0.8372881 0
## 291 0.8372881 0
## 292 0.8372881 0
## 293 0.8372881 0
## 294 0.8372881 0
## 295 0.8372881 0
## 296 0.8372881 0
## 297 0.8372881 0
## 298 0.8372881 0
## 299 0.8372881 0
## 300 0.8372881 0
## 301 0.8372881 0
## 302 0.8372881 0
## 303 0.8372881 0
## 304 0.8372881 0
## 305 0.8372881 0
## 306 0.8372881 0
## 307 0.8372881 0
## 308 0.8372881 0
## 309 0.8372881 0
## 310 0.8372881 0
## 311 0.8372881 0
## 312 0.8372881 0
## 313 0.8372881 0
## 314 0.8372881 0
## 315 0.8372881 0
## 316 0.8372881 0
## 317 0.8372881 0
## 318 0.8372881 0
## 319 0.8372881 0
## 320 0.8372881 0
## 321 0.8372881 0
## 322 0.8372881 0
## 323 0.8372881 0
## 324 0.8372881 0
## 325 0.8372881 0
## 326 0.8372881 0
## 327 0.8372881 0
## 328 0.8372881 0
## 329 0.8372881 0
## 330 0.8372881 0
## 331 0.8372881 0
## 332 0.8372881 0
## 333 0.8372881 0
## 334 0.8372881 0
## 335 0.8372881 0
## 336 0.8372881 0
## 337 0.8372881 0
## 338 0.8372881 0
## 339 0.8690476 1
## 340 0.8690476 1
## 341 0.8690476 1
## 342 0.8690476 1
## 343 0.8690476 1
## 344 0.8690476 1
## 345 0.8690476 1
## 346 0.8690476 1
## 347 0.8690476 1
## 348 0.8690476 1
## 349 0.8690476 1
## 350 0.8690476 1
## 351 0.8690476 1
## 352 0.8690476 1
## 353 0.8690476 1
## 354 0.8690476 1
## 355 0.8690476 1
## 356 0.8690476 1
## 357 0.8690476 1
## 358 0.8690476 1
## 359 0.8690476 1
## 360 0.8690476 1
## 361 0.8690476 1
## 362 0.8690476 1
## 363 0.8690476 1
## 364 0.8690476 1
## 365 0.8690476 1
## 366 0.8690476 1
## 367 0.8690476 1
## 368 0.8690476 1
## 369 0.8690476 1
## 370 0.8690476 1
## 371 0.8690476 1
## 372 0.8690476 1
## 373 0.8690476 1
## 374 0.8690476 1
## 375 0.8690476 1
## 376 0.8690476 1
## 377 0.8690476 1
## 378 0.8690476 1
## 379 0.8690476 1
## We can plot the data...
#ggplot(data=predicted.data ,aes(x=sex, y=probability.of.Survivor))+ geom_point(aes(color=sex), size=5) + xlab("Sex")
# + ylab("Predicted probability of getting heart disease")
xtabs(~ probability.of.Survivor + sex, data=predicted.data)
## sex
## probability.of.Survivor 0 1
## 0.837288135593219 295 0
## 0.869047619046891 0 84
# Inference
# The table shows that 295 females and 0 males are predicted to have a survival probability of 0.837 or lower. Additionally, 0 females and 84 males are predicted to have a survival probability of 0.869 or higher. This suggests that there may be a difference in the predicted survival rates between males and females, with females having higher predicted survival rates in this particular model.
logistic <- glm(Survivor ~ ., data=data, family="binomial")
summary(logistic)
##
## Call:
## glm(formula = Survivor ~ ., family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9390 0.1314 0.2733 0.5022 2.0329
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.871555 1.343279 0.649 0.5165
## Age -0.036605 0.019919 -1.838 0.0661 .
## Stage -0.682074 0.364806 -1.870 0.0615 .
## Tumor.Size 0.003787 0.010663 0.355 0.7225
## Regional.Node.Examined 0.010036 0.025469 0.394 0.6936
## Reginol.Node.Positive -0.085848 0.038773 -2.214 0.0268 *
## Survival.Months 0.070052 0.009895 7.079 1.45e-12 ***
## Sex -0.302243 0.424708 -0.712 0.4767
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 327.78 on 378 degrees of freedom
## Residual deviance: 221.79 on 371 degrees of freedom
## AIC: 237.79
##
## Number of Fisher Scoring iterations: 6
# In the output the coefficients for each predictor variable give us information about the strength and direction of the relationship between that variable and the response variable (Survivor in this case).
# This represents the log-odds of the response variable when all predictor variables are equal to zero. In this case, the intercept is not statistically significant,i.e there is no evidence of a significant difference in the log-odds of survival between men and women when all other predictor variables are equal to zero.
## Now calculate the overall "Pseudo R-squared" and its p-value
ll.null <- logistic$null.deviance/-2
ll.proposed <- logistic$deviance/-2
(ll.null - ll.proposed) / ll.null
## [1] 0.3233411
## The p-value for the R^2
1 - pchisq(2*(ll.proposed - ll.null), df=(length(logistic$coefficients)-1))
## [1] 0
predicted.data <- data.frame(probability.of.Survivor=logistic$fitted.values,Survivor=data$Survivor)
predicted.data <- predicted.data[order(predicted.data$probability.of.Survivor, decreasing=FALSE),]
predicted.data$rank <- 1:nrow(predicted.data)
## Lastly, we can plot the predicted probabilities for each sample having
## heart disease and color by whether or not they actually had heart disease
ggplot(data=predicted.data, aes(x=rank, y=probability.of.Survivor)) +
geom_point(aes(color=Survivor), alpha=1, shape=4, stroke=2) +
xlab("Index") +
ylab("Predicted probability of getting heart disease")
# From Caret
pdata <- predict(logistic,newdata=data,type="response" )
pdata
## 1 2 3 4 5 6 7
## 0.88831102 0.86578209 0.84995647 0.98116713 0.80044456 0.99045299 0.89662410
## 8 9 10 11 12 13 14
## 0.29775610 0.65207562 0.79641607 0.90355440 0.97497531 0.74200843 0.68591579
## 15 16 17 18 19 20 21
## 0.69263174 0.82862631 0.99269135 0.92431196 0.99557181 0.94929923 0.97116811
## 22 23 24 25 26 27 28
## 0.68917655 0.95357109 0.98978325 0.96206032 0.73883589 0.96647630 0.98749374
## 29 30 31 32 33 34 35
## 0.85766343 0.96120781 0.82133127 0.84593721 0.98745279 0.91255698 0.36377388
## 36 37 38 39 40 41 42
## 0.96678190 0.40571882 0.99489647 0.96146814 0.98903654 0.21995911 0.86185521
## 43 44 45 46 47 48 49
## 0.95137939 0.94644524 0.90420655 0.90687578 0.74927862 0.86320463 0.92542695
## 50 51 52 53 54 55 56
## 0.95014170 0.94399233 0.76562375 0.94213580 0.80863921 0.95550629 0.95580846
## 57 58 59 60 61 62 63
## 0.97837667 0.99809013 0.97326054 0.97377731 0.97978836 0.86460992 0.96943018
## 64 65 66 67 68 69 70
## 0.90313420 0.86901847 0.99740689 0.33053904 0.99080334 0.97395718 0.98365971
## 71 72 73 74 75 76 77
## 0.98583904 0.03415607 0.90057924 0.99134734 0.87098641 0.97547598 0.89889464
## 78 79 80 81 82 83 84
## 0.99486745 0.96107154 0.78788397 0.97204167 0.88877744 0.86234455 0.85705580
## 85 86 87 88 89 90 91
## 0.93554573 0.86087708 0.93122855 0.94382312 0.99022226 0.98491247 0.96005133
## 92 93 94 95 96 97 98
## 0.94212965 0.94261145 0.33001097 0.98220004 0.64680602 0.29074803 0.89981972
## 99 100 101 102 103 104 105
## 0.64330189 0.66323462 0.43857327 0.97829929 0.22354436 0.77211788 0.89353515
## 106 107 108 109 110 111 112
## 0.80265989 0.35159805 0.90097655 0.99604987 0.83947114 0.91983868 0.95123466
## 113 114 115 116 117 118 119
## 0.93580554 0.94443164 0.97992725 0.86139707 0.97816524 0.97616076 0.98448979
## 120 121 122 123 124 125 126
## 0.83772221 0.97517684 0.89367844 0.73041230 0.96781380 0.85789056 0.27683280
## 127 128 129 130 131 132 133
## 0.99416747 0.82470851 0.97439665 0.97971422 0.83090771 0.92734603 0.99208666
## 134 135 136 137 138 139 140
## 0.98894569 0.50400021 0.92675110 0.97890075 0.88246066 0.61178303 0.97977415
## 141 142 143 144 145 146 147
## 0.98548690 0.99720196 0.89262213 0.57376638 0.80487429 0.99295490 0.99313570
## 148 149 150 151 152 153 154
## 0.68855271 0.93082790 0.95519341 0.99753385 0.83012483 0.87936705 0.98994652
## 155 156 157 158 159 160 161
## 0.84511740 0.93693559 0.89759205 0.99728994 0.92864988 0.07629724 0.12665245
## 162 163 164 165 166 167 168
## 0.87357338 0.97760853 0.98801546 0.71860531 0.57395724 0.94541053 0.95169442
## 169 170 171 172 173 174 175
## 0.81115829 0.99531408 0.81837187 0.85206847 0.98585670 0.98230187 0.99203893
## 176 177 178 179 180 181 182
## 0.93941356 0.66874355 0.98138186 0.65941869 0.83593734 0.99168361 0.93283442
## 183 184 185 186 187 188 189
## 0.37473143 0.75758104 0.92327733 0.96005216 0.88497908 0.91845011 0.96076840
## 190 191 192 193 194 195 196
## 0.98449873 0.84622757 0.98505819 0.92065410 0.97088399 0.61522419 0.80090129
## 197 198 199 200 201 202 203
## 0.81281253 0.97721261 0.81447931 0.99354033 0.95033916 0.83701996 0.71002461
## 204 205 206 207 208 209 210
## 0.20809351 0.93143118 0.81240412 0.98383227 0.99216184 0.94837387 0.95335510
## 211 212 213 214 215 216 217
## 0.90373232 0.10518046 0.98864696 0.86704872 0.71379773 0.08775505 0.57255879
## 218 219 220 221 222 223 224
## 0.92880536 0.89346002 0.04082957 0.09889219 0.58087693 0.99766081 0.95996780
## 225 226 227 228 229 230 231
## 0.99102951 0.99713003 0.62543221 0.87658314 0.85045402 0.97165707 0.98171394
## 232 233 234 235 236 237 238
## 0.81064129 0.72862850 0.94182360 0.98913693 0.95130080 0.36966993 0.98288653
## 239 240 241 242 243 244 245
## 0.02174077 0.98060414 0.82812217 0.99146971 0.98903342 0.94197260 0.98017293
## 246 247 248 249 250 251 252
## 0.99446433 0.98936914 0.66627339 0.98706495 0.99255644 0.99453106 0.82242065
## 253 254 255 256 257 258 259
## 0.98060207 0.91375978 0.61162607 0.97553671 0.96866405 0.87868109 0.97747698
## 260 261 262 263 264 265 266
## 0.87893348 0.29218348 0.99449605 0.95271142 0.90451448 0.99249934 0.98481589
## 267 268 269 270 271 272 273
## 0.89835466 0.87093308 0.58773585 0.63242696 0.49196823 0.83193614 0.68670888
## 274 275 276 277 278 279 280
## 0.94137556 0.89307703 0.94393100 0.53608227 0.05693409 0.99113401 0.95267409
## 281 282 283 284 285 286 287
## 0.98468797 0.94039036 0.37185784 0.98448323 0.90550256 0.24720238 0.72675201
## 288 289 290 291 292 293 294
## 0.98625297 0.89119878 0.63437802 0.98400716 0.90345653 0.77885814 0.98778348
## 295 296 297 298 299 300 301
## 0.91702802 0.91325564 0.98546265 0.93578215 0.99228596 0.54815770 0.98997157
## 302 303 304 305 306 307 308
## 0.80034463 0.94299570 0.91836870 0.58938856 0.28189003 0.96577155 0.67227472
## 309 310 311 312 313 314 315
## 0.96597529 0.88409384 0.93935622 0.77276640 0.93453634 0.91675800 0.99105195
## 316 317 318 319 320 321 322
## 0.95223994 0.86712206 0.96565703 0.50066308 0.72889107 0.99583510 0.94848242
## 323 324 325 326 327 328 329
## 0.87796387 0.96507921 0.93508119 0.97104152 0.98740873 0.97744406 0.91344598
## 330 331 332 333 334 335 336
## 0.95111325 0.99381680 0.26819322 0.99546956 0.96101694 0.92390739 0.98373194
## 337 338 339 340 341 342 343
## 0.85776421 0.82997707 0.98581296 0.84399168 0.96333508 0.89227749 0.82372278
## 344 345 346 347 348 349 350
## 0.98502493 0.87703204 0.81417199 0.99515846 0.99001685 0.90448172 0.97387529
## 351 352 353 354 355 356 357
## 0.98651039 0.80786933 0.71501849 0.99461920 0.99589689 0.70750322 0.91091899
## 358 359 360 361 362 363 364
## 0.62535931 0.97056232 0.96490666 0.71666186 0.99606075 0.51296788 0.98668537
## 365 366 367 368 369 370 371
## 0.99721659 0.91993048 0.97796833 0.92115206 0.98721952 0.95174672 0.93886043
## 372 373 374 375 376 377 378
## 0.63916542 0.99036699 0.71545376 0.75885710 0.93652006 0.54170579 0.97656218
## 379
## 0.97452829
data$Survivor
## [1] 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1
## [112] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0
## [149] 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1
## [186] 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
## [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0
## [371] 1 0 1 1 1 1 1 1 1
pdataF <- as.factor(ifelse(test=as.numeric(pdata>0.5) == 0, yes="Alive", no="Dead"))
#From e1071::
#confusionMatrix(pdataF, data$Survivor)
# From pROC
roc(data$Survivor,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
par(pty = "s")
roc(data$Survivor,logistic$fitted.values,plot=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
## NOTE: By default, roc() uses specificity on the x-axis and the values range
## from 1 to 0. This makes the graph look like what we would expect, but the
## x-axis itself might induce a headache. To use 1-specificity (i.e. the
## False Positive Rate) on the x-axis, set "legacy.axes" to TRUE.
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage")
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage")
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 0.8596
## If we want to find out the optimal threshold we can store the
## data used to make the ROC graph in a variable...
roc.info <- roc(data$Survivor, logistic$fitted.values, legacy.axes=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
str(roc.info)
## List of 15
## $ percent : logi FALSE
## $ sensitivities : num [1:380] 1 1 1 1 1 ...
## $ specificities : num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
## $ thresholds : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
## $ direction : chr "<"
## $ cases : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
## ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
## $ controls : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
## ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
## $ fun.sesp :function (thresholds, controls, cases, direction)
## $ auc : 'auc' num 0.86
## ..- attr(*, "partial.auc")= logi FALSE
## ..- attr(*, "percent")= logi FALSE
## ..- attr(*, "roc")=List of 15
## .. ..$ percent : logi FALSE
## .. ..$ sensitivities : num [1:380] 1 1 1 1 1 ...
## .. ..$ specificities : num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
## .. ..$ thresholds : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
## .. ..$ direction : chr "<"
## .. ..$ cases : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
## .. .. ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
## .. ..$ controls : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
## .. .. ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
## .. ..$ fun.sesp :function (thresholds, controls, cases, direction)
## .. ..$ auc : 'auc' num 0.86
## .. .. ..- attr(*, "partial.auc")= logi FALSE
## .. .. ..- attr(*, "percent")= logi FALSE
## .. .. ..- attr(*, "roc")=List of 8
## .. .. .. ..$ percent : logi FALSE
## .. .. .. ..$ sensitivities: num [1:380] 1 1 1 1 1 ...
## .. .. .. ..$ specificities: num [1:380] 0 0.0169 0.0339 0.0508 0.0678 ...
## .. .. .. ..$ thresholds : num [1:380] -Inf 0.0279 0.0375 0.0489 0.0666 ...
## .. .. .. ..$ direction : chr "<"
## .. .. .. ..$ cases : Named num [1:320] 0.888 0.866 0.85 0.981 0.8 ...
## .. .. .. .. ..- attr(*, "names")= chr [1:320] "1" "2" "3" "4" ...
## .. .. .. ..$ controls : Named num [1:59] 0.298 0.904 0.22 0.749 0.869 ...
## .. .. .. .. ..- attr(*, "names")= chr [1:59] "8" "11" "41" "47" ...
## .. .. .. ..$ fun.sesp :function (thresholds, controls, cases, direction)
## .. .. .. ..- attr(*, "class")= chr "roc"
## .. ..$ call : language roc.default(response = data$Survivor, predictor = logistic$fitted.values, legacy.axes = TRUE)
## .. ..$ original.predictor: Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
## .. .. ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
## .. ..$ original.response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## .. ..$ predictor : Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
## .. .. ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
## .. ..$ response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## .. ..$ levels : chr [1:2] "0" "1"
## .. ..- attr(*, "class")= chr "roc"
## $ call : language roc.default(response = data$Survivor, predictor = logistic$fitted.values, legacy.axes = TRUE)
## $ original.predictor: Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
## ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
## $ original.response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## $ predictor : Named num [1:379] 0.888 0.866 0.85 0.981 0.8 ...
## ..- attr(*, "names")= chr [1:379] "1" "2" "3" "4" ...
## $ response : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## $ levels : chr [1:2] "0" "1"
## - attr(*, "class")= chr "roc"
## tpp = true positive percentage
## fpp = false positive precentage
roc.df <- data.frame(tpp=roc.info$sensitivities*100, fpp=(1 - roc.info$specificities)*100,thresholds=roc.info$thresholds)
roc.df
## tpp fpp thresholds
## 1 100.0000 100.000000 -Inf
## 2 100.0000 98.305085 0.02794842
## 3 100.0000 96.610169 0.03749282
## 4 100.0000 94.915254 0.04888183
## 5 100.0000 93.220339 0.06661567
## 6 100.0000 91.525424 0.08202615
## 7 100.0000 89.830508 0.09332362
## 8 100.0000 88.135593 0.10203633
## 9 100.0000 86.440678 0.11591645
## 10 99.6875 86.440678 0.16737298
## 11 99.6875 84.745763 0.21402631
## 12 99.6875 83.050847 0.22175174
## 13 99.3750 83.050847 0.23537337
## 14 99.3750 81.355932 0.25769780
## 15 99.3750 79.661017 0.27251301
## 16 99.3750 77.966102 0.27936141
## 17 99.3750 76.271186 0.28631903
## 18 99.3750 74.576271 0.29146575
## 19 99.0625 74.576271 0.29496979
## 20 99.0625 72.881356 0.31388354
## 21 99.0625 71.186441 0.33027501
## 22 99.0625 69.491525 0.34106855
## 23 99.0625 67.796610 0.35768597
## 24 98.7500 67.796610 0.36672190
## 25 98.4375 67.796610 0.37076389
## 26 98.4375 66.101695 0.37329464
## 27 98.4375 64.406780 0.39022512
## 28 98.1250 64.406780 0.42214605
## 29 98.1250 62.711864 0.46527075
## 30 98.1250 61.016949 0.49631565
## 31 97.8125 61.016949 0.50233165
## 32 97.8125 59.322034 0.50848405
## 33 97.8125 57.627119 0.52452507
## 34 97.5000 57.627119 0.53889403
## 35 97.1875 57.627119 0.54493174
## 36 96.8750 57.627119 0.56035824
## 37 96.8750 55.932203 0.57316259
## 38 96.8750 54.237288 0.57386181
## 39 96.5625 54.237288 0.57741708
## 40 96.5625 52.542373 0.58430639
## 41 96.5625 50.847458 0.58856221
## 42 96.2500 50.847458 0.60050732
## 43 95.9375 50.847458 0.61170455
## 44 95.9375 49.152542 0.61350361
## 45 95.6250 49.152542 0.62029175
## 46 95.6250 47.457627 0.62539576
## 47 95.3125 47.457627 0.62892959
## 48 95.0000 47.457627 0.63340249
## 49 95.0000 45.762712 0.63677172
## 50 95.0000 44.067797 0.64123365
## 51 95.0000 42.372881 0.64505395
## 52 94.6875 42.372881 0.64944082
## 53 94.3750 42.372881 0.65574715
## 54 94.0625 42.372881 0.66132665
## 55 93.7500 42.372881 0.66475400
## 56 93.7500 40.677966 0.66750847
## 57 93.7500 38.983051 0.67050913
## 58 93.4375 38.983051 0.67909525
## 59 93.1250 38.983051 0.68631233
## 60 92.8125 38.983051 0.68763079
## 61 92.8125 37.288136 0.68886463
## 62 92.5000 37.288136 0.69090415
## 63 92.1875 37.288136 0.70006748
## 64 91.8750 37.288136 0.70876391
## 65 91.8750 35.593220 0.71191117
## 66 91.5625 35.593220 0.71440811
## 67 91.2500 35.593220 0.71523613
## 68 90.9375 35.593220 0.71605781
## 69 90.6250 35.593220 0.71763359
## 70 90.3125 35.593220 0.72267866
## 71 90.0000 35.593220 0.72769025
## 72 89.6875 35.593220 0.72875978
## 73 89.3750 35.593220 0.72965169
## 74 89.0625 35.593220 0.73462410
## 75 88.7500 35.593220 0.74042216
## 76 88.4375 35.593220 0.74564353
## 77 88.4375 33.898305 0.75342983
## 78 88.1250 33.898305 0.75821907
## 79 87.8125 33.898305 0.76224042
## 80 87.5000 33.898305 0.76887082
## 81 87.5000 32.203390 0.77244214
## 82 87.1875 32.203390 0.77581227
## 83 87.1875 30.508475 0.78337105
## 84 86.8750 30.508475 0.79215002
## 85 86.5625 30.508475 0.79838035
## 86 86.2500 30.508475 0.80039459
## 87 85.9375 30.508475 0.80067293
## 88 85.6250 30.508475 0.80178059
## 89 85.3125 30.508475 0.80376709
## 90 85.3125 28.813559 0.80637181
## 91 85.0000 28.813559 0.80825427
## 92 84.6875 28.813559 0.80964025
## 93 84.3750 28.813559 0.81089979
## 94 84.0625 28.813559 0.81178120
## 95 83.7500 28.813559 0.81260832
## 96 83.4375 28.813559 0.81349226
## 97 83.1250 28.813559 0.81432565
## 98 82.8125 28.813559 0.81642559
## 99 82.8125 27.118644 0.81985157
## 100 82.5000 27.118644 0.82187596
## 101 82.1875 27.118644 0.82307171
## 102 81.8750 27.118644 0.82421564
## 103 81.5625 27.118644 0.82641534
## 104 81.5625 25.423729 0.82837424
## 105 81.2500 25.423729 0.82930169
## 106 80.9375 25.423729 0.83005095
## 107 80.6250 25.423729 0.83051627
## 108 80.3125 25.423729 0.83142192
## 109 80.0000 25.423729 0.83393674
## 110 80.0000 23.728814 0.83647865
## 111 79.6875 23.728814 0.83737108
## 112 79.3750 23.728814 0.83859668
## 113 79.0625 23.728814 0.84173141
## 114 78.7500 23.728814 0.84455454
## 115 78.4375 23.728814 0.84552731
## 116 78.1250 23.728814 0.84608239
## 117 77.8125 23.728814 0.84809202
## 118 77.5000 23.728814 0.85020525
## 119 77.1875 23.728814 0.85126125
## 120 76.8750 23.728814 0.85456213
## 121 76.5625 23.728814 0.85735961
## 122 76.2500 23.728814 0.85771382
## 123 75.9375 23.728814 0.85782739
## 124 75.6250 23.728814 0.85938382
## 125 75.3125 23.728814 0.86113708
## 126 75.0000 23.728814 0.86162614
## 127 74.6875 23.728814 0.86209988
## 128 74.3750 23.728814 0.86277459
## 129 74.0625 23.728814 0.86390728
## 130 73.7500 23.728814 0.86519600
## 131 73.4375 23.728814 0.86641540
## 132 73.1250 23.728814 0.86708539
## 133 72.8125 23.728814 0.86807027
## 134 72.8125 22.033898 0.86997578
## 135 72.5000 22.033898 0.87095974
## 136 72.1875 22.033898 0.87227989
## 137 71.8750 22.033898 0.87507826
## 138 71.5625 22.033898 0.87680759
## 139 71.2500 22.033898 0.87749796
## 140 70.9375 22.033898 0.87832248
## 141 70.6250 22.033898 0.87880729
## 142 70.3125 22.033898 0.87915027
## 143 70.3125 20.338983 0.88091386
## 144 70.3125 18.644068 0.88327725
## 145 70.0000 18.644068 0.88453646
## 146 69.6875 18.644068 0.88664505
## 147 69.3750 18.644068 0.88854423
## 148 69.0625 18.644068 0.88998811
## 149 68.7500 18.644068 0.89173813
## 150 68.4375 18.644068 0.89244981
## 151 68.1250 18.644068 0.89284958
## 152 67.8125 18.644068 0.89326852
## 153 67.5000 18.644068 0.89349759
## 154 67.1875 18.644068 0.89360680
## 155 66.8750 18.644068 0.89515127
## 156 66.5625 18.644068 0.89710808
## 157 66.2500 18.644068 0.89797335
## 158 65.9375 18.644068 0.89862465
## 159 65.6250 18.644068 0.89935718
## 160 65.3125 18.644068 0.90019948
## 161 65.0000 18.644068 0.90077789
## 162 64.6875 18.644068 0.90205537
## 163 64.3750 18.644068 0.90329536
## 164 64.0625 18.644068 0.90350546
## 165 64.0625 16.949153 0.90364336
## 166 63.7500 16.949153 0.90396943
## 167 63.4375 16.949153 0.90434414
## 168 63.1250 16.949153 0.90449810
## 169 63.1250 15.254237 0.90500852
## 170 62.8125 15.254237 0.90618917
## 171 62.5000 15.254237 0.90889738
## 172 62.1875 15.254237 0.91173798
## 173 61.8750 15.254237 0.91290631
## 174 61.5625 15.254237 0.91335081
## 175 61.2500 15.254237 0.91360288
## 176 60.9375 15.254237 0.91525889
## 177 60.9375 13.559322 0.91689301
## 178 60.6250 13.559322 0.91769836
## 179 60.3125 13.559322 0.91840941
## 180 60.0000 13.559322 0.91914440
## 181 59.6875 13.559322 0.91988458
## 182 59.3750 13.559322 0.92029229
## 183 59.0625 13.559322 0.92090308
## 184 58.7500 13.559322 0.92221470
## 185 58.4375 13.559322 0.92359236
## 186 58.1250 13.559322 0.92410967
## 187 57.8125 13.559322 0.92486945
## 188 57.5000 13.559322 0.92608903
## 189 57.5000 11.864407 0.92704857
## 190 57.1875 11.864407 0.92799795
## 191 56.8750 11.864407 0.92872762
## 192 56.5625 11.864407 0.92981663
## 193 56.2500 11.864407 0.93102822
## 194 55.9375 11.864407 0.93132986
## 195 55.6250 11.864407 0.93213280
## 196 55.6250 10.169492 0.93368538
## 197 55.3125 10.169492 0.93480876
## 198 55.0000 10.169492 0.93531346
## 199 54.6875 10.169492 0.93566394
## 200 54.3750 10.169492 0.93579385
## 201 54.0625 10.169492 0.93616280
## 202 53.7500 10.169492 0.93672782
## 203 53.4375 10.169492 0.93789801
## 204 53.1250 10.169492 0.93910832
## 205 52.8125 10.169492 0.93938489
## 206 52.5000 10.169492 0.93990196
## 207 52.1875 10.169492 0.94088296
## 208 51.8750 10.169492 0.94159958
## 209 51.5625 10.169492 0.94189810
## 210 51.2500 10.169492 0.94205113
## 211 50.9375 10.169492 0.94213272
## 212 50.6250 10.169492 0.94237362
## 213 50.6250 8.474576 0.94280358
## 214 50.3125 8.474576 0.94340941
## 215 50.0000 8.474576 0.94387706
## 216 49.6875 8.474576 0.94396166
## 217 49.3750 8.474576 0.94421199
## 218 49.0625 8.474576 0.94492109
## 219 48.7500 8.474576 0.94592788
## 220 48.4375 8.474576 0.94740955
## 221 48.1250 8.474576 0.94842814
## 222 47.8125 8.474576 0.94889083
## 223 47.5000 8.474576 0.94972047
## 224 47.1875 8.474576 0.95024043
## 225 46.8750 8.474576 0.95072621
## 226 46.5625 8.474576 0.95117396
## 227 46.5625 6.779661 0.95126773
## 228 46.2500 6.779661 0.95134010
## 229 45.9375 6.779661 0.95153690
## 230 45.6250 6.779661 0.95172057
## 231 45.6250 5.084746 0.95199333
## 232 45.3125 5.084746 0.95245701
## 233 45.0000 5.084746 0.95269275
## 234 44.6875 5.084746 0.95303326
## 235 44.3750 5.084746 0.95346310
## 236 44.0625 5.084746 0.95438225
## 237 43.7500 5.084746 0.95534985
## 238 43.4375 5.084746 0.95565737
## 239 43.1250 5.084746 0.95788813
## 240 42.8125 5.084746 0.96000957
## 241 42.8125 3.389831 0.96005175
## 242 42.5000 3.389831 0.96041028
## 243 42.5000 1.694915 0.96089267
## 244 42.1875 1.694915 0.96104424
## 245 41.8750 1.694915 0.96113968
## 246 41.5625 1.694915 0.96133798
## 247 41.2500 1.694915 0.96176423
## 248 40.9375 1.694915 0.96269770
## 249 40.6250 1.694915 0.96412087
## 250 40.3125 1.694915 0.96499294
## 251 40.0000 1.694915 0.96536812
## 252 39.6875 1.694915 0.96571429
## 253 39.3750 1.694915 0.96587342
## 254 39.0625 1.694915 0.96622579
## 255 38.7500 1.694915 0.96662910
## 256 38.4375 1.694915 0.96729785
## 257 38.1250 1.694915 0.96823893
## 258 37.8125 1.694915 0.96904711
## 259 37.5000 1.694915 0.96999625
## 260 37.1875 1.694915 0.97072316
## 261 36.8750 1.694915 0.97096276
## 262 36.5625 1.694915 0.97110481
## 263 36.2500 1.694915 0.97141259
## 264 35.9375 1.694915 0.97184937
## 265 35.6250 1.694915 0.97265111
## 266 35.3125 1.694915 0.97351892
## 267 35.0000 1.694915 0.97382630
## 268 34.6875 1.694915 0.97391623
## 269 34.3750 1.694915 0.97417692
## 270 34.0625 1.694915 0.97446247
## 271 33.7500 1.694915 0.97475180
## 272 33.4375 1.694915 0.97507608
## 273 33.1250 1.694915 0.97532641
## 274 32.8125 1.694915 0.97550634
## 275 32.5000 1.694915 0.97584873
## 276 32.1875 1.694915 0.97636147
## 277 31.8750 1.694915 0.97688740
## 278 31.5625 1.694915 0.97732834
## 279 31.2500 1.694915 0.97746052
## 280 30.9375 1.694915 0.97754275
## 281 30.6250 1.694915 0.97778843
## 282 30.3125 1.694915 0.97806679
## 283 30.0000 1.694915 0.97823226
## 284 29.6875 1.694915 0.97833798
## 285 29.3750 1.694915 0.97863871
## 286 29.0625 1.694915 0.97930748
## 287 28.7500 1.694915 0.97974418
## 288 28.4375 1.694915 0.97978125
## 289 28.1250 1.694915 0.97985780
## 290 27.8125 1.694915 0.98005009
## 291 27.5000 1.694915 0.98038750
## 292 27.1875 1.694915 0.98060311
## 293 26.8750 1.694915 0.98088564
## 294 26.5625 1.694915 0.98127450
## 295 26.2500 1.694915 0.98154790
## 296 25.9375 1.694915 0.98195699
## 297 25.6250 1.694915 0.98225095
## 298 25.3125 1.694915 0.98259420
## 299 25.0000 1.694915 0.98327312
## 300 24.6875 1.694915 0.98369583
## 301 24.3750 1.694915 0.98378211
## 302 24.0625 1.694915 0.98391972
## 303 23.7500 1.694915 0.98424520
## 304 23.4375 1.694915 0.98448651
## 305 23.1250 1.694915 0.98449426
## 306 22.8125 1.694915 0.98459335
## 307 22.5000 1.694915 0.98475193
## 308 22.1875 1.694915 0.98486418
## 309 21.8750 1.694915 0.98496870
## 310 21.5625 1.694915 0.98504156
## 311 21.2500 1.694915 0.98526042
## 312 20.9375 1.694915 0.98547478
## 313 20.6250 1.694915 0.98564993
## 314 20.3125 1.694915 0.98582600
## 315 20.0000 1.694915 0.98584787
## 316 19.6875 1.694915 0.98605484
## 317 19.3750 1.694915 0.98638168
## 318 19.0625 1.694915 0.98659788
## 319 19.0625 0.000000 0.98687516
## 320 18.7500 0.000000 0.98714224
## 321 18.4375 0.000000 0.98731413
## 322 18.1250 0.000000 0.98743076
## 323 17.8125 0.000000 0.98747326
## 324 17.5000 0.000000 0.98763861
## 325 17.1875 0.000000 0.98789947
## 326 16.8750 0.000000 0.98833121
## 327 16.5625 0.000000 0.98879632
## 328 16.2500 0.000000 0.98898955
## 329 15.9375 0.000000 0.98903498
## 330 15.6250 0.000000 0.98908674
## 331 15.3125 0.000000 0.98925304
## 332 15.0000 0.000000 0.98957620
## 333 14.6875 0.000000 0.98986489
## 334 14.3750 0.000000 0.98995905
## 335 14.0625 0.000000 0.98999421
## 336 13.7500 0.000000 0.99011956
## 337 13.4375 0.000000 0.99029463
## 338 13.1250 0.000000 0.99040999
## 339 12.8125 0.000000 0.99062816
## 340 12.5000 0.000000 0.99091642
## 341 12.1875 0.000000 0.99104073
## 342 11.8750 0.000000 0.99109298
## 343 11.5625 0.000000 0.99124068
## 344 11.2500 0.000000 0.99140853
## 345 10.9375 0.000000 0.99157666
## 346 10.6250 0.000000 0.99186127
## 347 10.3125 0.000000 0.99206280
## 348 10.0000 0.000000 0.99212425
## 349 9.6875 0.000000 0.99222390
## 350 9.3750 0.000000 0.99239265
## 351 9.0625 0.000000 0.99252789
## 352 8.7500 0.000000 0.99262390
## 353 8.4375 0.000000 0.99282313
## 354 8.1250 0.000000 0.99304530
## 355 7.8125 0.000000 0.99333801
## 356 7.5000 0.000000 0.99367856
## 357 7.1875 0.000000 0.99399213
## 358 6.8750 0.000000 0.99431590
## 359 6.5625 0.000000 0.99448019
## 360 6.2500 0.000000 0.99451356
## 361 5.9375 0.000000 0.99457513
## 362 5.6250 0.000000 0.99474332
## 363 5.3125 0.000000 0.99488196
## 364 5.0000 0.000000 0.99502747
## 365 4.6875 0.000000 0.99523627
## 366 4.3750 0.000000 0.99539182
## 367 4.0625 0.000000 0.99552069
## 368 3.7500 0.000000 0.99570345
## 369 3.4375 0.000000 0.99586599
## 370 3.1250 0.000000 0.99597338
## 371 2.8125 0.000000 0.99605531
## 372 2.5000 0.000000 0.99659539
## 373 2.1875 0.000000 0.99716599
## 374 1.8750 0.000000 0.99720927
## 375 1.5625 0.000000 0.99725327
## 376 1.2500 0.000000 0.99734842
## 377 0.9375 0.000000 0.99747037
## 378 0.6250 0.000000 0.99759733
## 379 0.3125 0.000000 0.99787547
## 380 0.0000 0.000000 Inf
head(roc.df)
## tpp fpp thresholds
## 1 100 100.00000 -Inf
## 2 100 98.30508 0.02794842
## 3 100 96.61017 0.03749282
## 4 100 94.91525 0.04888183
## 5 100 93.22034 0.06661567
## 6 100 91.52542 0.08202615
## head() will show us the values for the upper right-hand corner of the ROC graph, when the threshold is so low
## (negative infinity) that every single sample is called "obese".
## Thus TPP = 100% and FPP = 100%
tail(roc.df)
## tpp fpp thresholds
## 375 1.5625 0 0.9972533
## 376 1.2500 0 0.9973484
## 377 0.9375 0 0.9974704
## 378 0.6250 0 0.9975973
## 379 0.3125 0 0.9978755
## 380 0.0000 0 Inf
## tail() will show us the values for the lower left-hand corner
## of the ROC graph, when the threshold is so high (infinity)
## that every single sample is called "not obese".
## Thus, TPP = 0% and FPP = 0%
## now let's look at the thresholds between TPP 60% and 80%
roc.df[roc.df$tpp > 60 & roc.df$tpp < 80,]
## tpp fpp thresholds
## 111 79.6875 23.72881 0.8373711
## 112 79.3750 23.72881 0.8385967
## 113 79.0625 23.72881 0.8417314
## 114 78.7500 23.72881 0.8445545
## 115 78.4375 23.72881 0.8455273
## 116 78.1250 23.72881 0.8460824
## 117 77.8125 23.72881 0.8480920
## 118 77.5000 23.72881 0.8502052
## 119 77.1875 23.72881 0.8512612
## 120 76.8750 23.72881 0.8545621
## 121 76.5625 23.72881 0.8573596
## 122 76.2500 23.72881 0.8577138
## 123 75.9375 23.72881 0.8578274
## 124 75.6250 23.72881 0.8593838
## 125 75.3125 23.72881 0.8611371
## 126 75.0000 23.72881 0.8616261
## 127 74.6875 23.72881 0.8620999
## 128 74.3750 23.72881 0.8627746
## 129 74.0625 23.72881 0.8639073
## 130 73.7500 23.72881 0.8651960
## 131 73.4375 23.72881 0.8664154
## 132 73.1250 23.72881 0.8670854
## 133 72.8125 23.72881 0.8680703
## 134 72.8125 22.03390 0.8699758
## 135 72.5000 22.03390 0.8709597
## 136 72.1875 22.03390 0.8722799
## 137 71.8750 22.03390 0.8750783
## 138 71.5625 22.03390 0.8768076
## 139 71.2500 22.03390 0.8774980
## 140 70.9375 22.03390 0.8783225
## 141 70.6250 22.03390 0.8788073
## 142 70.3125 22.03390 0.8791503
## 143 70.3125 20.33898 0.8809139
## 144 70.3125 18.64407 0.8832773
## 145 70.0000 18.64407 0.8845365
## 146 69.6875 18.64407 0.8866451
## 147 69.3750 18.64407 0.8885442
## 148 69.0625 18.64407 0.8899881
## 149 68.7500 18.64407 0.8917381
## 150 68.4375 18.64407 0.8924498
## 151 68.1250 18.64407 0.8928496
## 152 67.8125 18.64407 0.8932685
## 153 67.5000 18.64407 0.8934976
## 154 67.1875 18.64407 0.8936068
## 155 66.8750 18.64407 0.8951513
## 156 66.5625 18.64407 0.8971081
## 157 66.2500 18.64407 0.8979734
## 158 65.9375 18.64407 0.8986246
## 159 65.6250 18.64407 0.8993572
## 160 65.3125 18.64407 0.9001995
## 161 65.0000 18.64407 0.9007779
## 162 64.6875 18.64407 0.9020554
## 163 64.3750 18.64407 0.9032954
## 164 64.0625 18.64407 0.9035055
## 165 64.0625 16.94915 0.9036434
## 166 63.7500 16.94915 0.9039694
## 167 63.4375 16.94915 0.9043441
## 168 63.1250 16.94915 0.9044981
## 169 63.1250 15.25424 0.9050085
## 170 62.8125 15.25424 0.9061892
## 171 62.5000 15.25424 0.9088974
## 172 62.1875 15.25424 0.9117380
## 173 61.8750 15.25424 0.9129063
## 174 61.5625 15.25424 0.9133508
## 175 61.2500 15.25424 0.9136029
## 176 60.9375 15.25424 0.9152589
## 177 60.9375 13.55932 0.9168930
## 178 60.6250 13.55932 0.9176984
## 179 60.3125 13.55932 0.9184094
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 85.96%
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 85.96%
roc(data$Survivor,logistic$fitted.values,plot=TRUE, legacy.axes=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, percent=TRUE, print.auc=TRUE, partial.auc=c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x=45)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE, partial.auc = c(100, 90), auc.polygon = TRUE, auc.polygon.col = "#377eb822", print.auc.x = 45)
##
## Data: logistic$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Partial area under the curve (specificity 100%-90%): 4.104%
# Lets do two roc plots to understand which model is better
roc(data$Survivor, logistic_simple$fitted.values, plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Postive Percentage", col="#377eb8", lwd=4, print.auc=TRUE)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
##
## Call:
## roc.default(response = data$Survivor, predictor = logistic_simple$fitted.values, percent = TRUE, plot = TRUE, legacy.axes = TRUE, xlab = "False Positive Percentage", ylab = "True Postive Percentage", col = "#377eb8", lwd = 4, print.auc = TRUE)
##
## Data: logistic_simple$fitted.values in 59 controls (data$Survivor 0) < 320 cases (data$Survivor 1).
## Area under the curve: 52.08%
# Lets add the other graph
plot.roc(data$Survivor, logistic$fitted.values, percent=TRUE, col="#4daf4a", lwd=4, print.auc=TRUE, add=TRUE, print.auc.y=40)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
legend("bottomright", legend=c("Simple", "Non Simple"), col=c("#377eb8", "#4daf4a"), lwd=4)
# ggplots
library(ggplot2)
library(lattice)
library(ggridges)
library(ggvis)
library(ggthemes)
library(cowplot)
library(gapminder)
library(gganimate)
library(dplyr)
library(tidyverse)
library(grid)
library(gridExtra)
library(RColorBrewer)
library(readr)
Cancer<- read_csv("~/Downloads/BC.csv")
## Rows: 379 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): Survivor, Age, Stage, Tumor.Size, Regional.Node.Examined, Reginol.N...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Cancer
## # A tibble: 379 × 8
## Survivor Age Stage Tumor.Size Regional.Node.Examined Regino…¹ Survi…² Sex
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 68 1 4 24 1 60 0
## 2 1 50 2 35 14 5 62 0
## 3 1 58 3 63 14 7 75 0
## 4 1 58 1 18 2 1 84 0
## 5 1 47 2 41 3 1 50 0
## 6 1 51 1 20 18 2 89 0
## 7 1 51 1 8 11 1 54 0
## 8 0 40 2 30 9 1 14 0
## 9 1 40 4 103 20 18 70 0
## 10 1 69 4 32 21 12 92 0
## # … with 369 more rows, and abbreviated variable names ¹​Reginol.Node.Positive,
## # ²​Survival.Months
str(Cancer)
## spc_tbl_ [379 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Survivor : num [1:379] 1 1 1 1 1 1 1 0 1 1 ...
## $ Age : num [1:379] 68 50 58 58 47 51 51 40 40 69 ...
## $ Stage : num [1:379] 1 2 3 1 2 1 1 2 4 4 ...
## $ Tumor.Size : num [1:379] 4 35 63 18 41 20 8 30 103 32 ...
## $ Regional.Node.Examined: num [1:379] 24 14 14 2 3 18 11 9 20 21 ...
## $ Reginol.Node.Positive : num [1:379] 1 5 7 1 1 2 1 1 18 12 ...
## $ Survival.Months : num [1:379] 60 62 75 84 50 89 54 14 70 92 ...
## $ Sex : num [1:379] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "spec")=
## .. cols(
## .. Survivor = col_double(),
## .. Age = col_double(),
## .. Stage = col_double(),
## .. Tumor.Size = col_double(),
## .. Regional.Node.Examined = col_double(),
## .. Reginol.Node.Positive = col_double(),
## .. Survival.Months = col_double(),
## .. Sex = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
# Scatter plot
ggplot(Cancer, aes(x=Age,y=Stage))+geom_point(aes(color=Survivor))
## We can see from the graph that there are no deaths for any age group in stage 1 of cancer.
## In stage 2 there are negligle deaths.
## In stage 3 30-40 and 50-60 years age group there are few deaths.
## In stage 4 death rates are more.
ggplot(Cancer, aes(x=Stage,y=Tumor.Size))+geom_point(aes(color=Survivor))
## From this graph we can infere that death rates are more in stage 3 and 4 for tumor size 50 and above.
ggplot(Cancer, aes(x=Age,y=Survival.Months)) + facet_wrap(~Stage) + geom_point(aes(color=Survivor))
# Histogram
ggplot(Cancer, aes(Stage))+geom_histogram(fill='coral', color='white',bins=10)
ggplot(Cancer, aes(Sex))+geom_histogram(aes(fill=after_stat(count)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# We can see from this graph that stage 1 & 2 patients are more.
# Bar chart
ggplot(Cancer, aes(Survivor))+ geom_bar(position="stack", fill='seagreen')
## Number of survivors are more compared to non-survivors.
ggplot(Cancer, aes(Stage)) + facet_grid(.~Survivor) + geom_bar(position="dodge",fill='violet')
# box plot
ggplot(Cancer, aes(x=Survivor,y=Age)) + geom_boxplot()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
ggplot(Cancer, aes(x=Survival.Months,y=Stage)) + geom_boxplot() + coord_flip()
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
# hexbin
ggplot(Cancer, aes(x=Age, y=Stage)) + geom_hex()
